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Research Design | Step-by-Step Guide with Examples

Published on 5 May 2022 by Shona McCombes . Revised on 20 March 2023.

A research design is a strategy for answering your research question  using empirical data. Creating a research design means making decisions about:

• Your overall aims and approach
• The type of research design you’ll use
• Your sampling methods or criteria for selecting subjects
• Your data collection methods
• The procedures you’ll follow to collect data
• Your data analysis methods

A well-planned research design helps ensure that your methods match your research aims and that you use the right kind of analysis for your data.

Table of contents

Step 1: consider your aims and approach, step 2: choose a type of research design, step 3: identify your population and sampling method, step 4: choose your data collection methods, step 5: plan your data collection procedures, step 6: decide on your data analysis strategies, frequently asked questions.

• Introduction

Before you can start designing your research, you should already have a clear idea of the research question you want to investigate.

There are many different ways you could go about answering this question. Your research design choices should be driven by your aims and priorities – start by thinking carefully about what you want to achieve.

The first choice you need to make is whether you’ll take a qualitative or quantitative approach.

Qualitative research designs tend to be more flexible and inductive , allowing you to adjust your approach based on what you find throughout the research process.

Quantitative research designs tend to be more fixed and deductive , with variables and hypotheses clearly defined in advance of data collection.

It’s also possible to use a mixed methods design that integrates aspects of both approaches. By combining qualitative and quantitative insights, you can gain a more complete picture of the problem you’re studying and strengthen the credibility of your conclusions.

Practical and ethical considerations when designing research

As well as scientific considerations, you need to think practically when designing your research. If your research involves people or animals, you also need to consider research ethics .

• How much time do you have to collect data and write up the research?
• Will you be able to gain access to the data you need (e.g., by travelling to a specific location or contacting specific people)?
• Do you have the necessary research skills (e.g., statistical analysis or interview techniques)?
• Will you need ethical approval ?

At each stage of the research design process, make sure that your choices are practically feasible.

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Within both qualitative and quantitative approaches, there are several types of research design to choose from. Each type provides a framework for the overall shape of your research.

Types of quantitative research designs

Quantitative designs can be split into four main types. Experimental and   quasi-experimental designs allow you to test cause-and-effect relationships, while descriptive and correlational designs allow you to measure variables and describe relationships between them.

With descriptive and correlational designs, you can get a clear picture of characteristics, trends, and relationships as they exist in the real world. However, you can’t draw conclusions about cause and effect (because correlation doesn’t imply causation ).

Experiments are the strongest way to test cause-and-effect relationships without the risk of other variables influencing the results. However, their controlled conditions may not always reflect how things work in the real world. They’re often also more difficult and expensive to implement.

Types of qualitative research designs

Qualitative designs are less strictly defined. This approach is about gaining a rich, detailed understanding of a specific context or phenomenon, and you can often be more creative and flexible in designing your research.

The table below shows some common types of qualitative design. They often have similar approaches in terms of data collection, but focus on different aspects when analysing the data.

Your research design should clearly define who or what your research will focus on, and how you’ll go about choosing your participants or subjects.

In research, a population is the entire group that you want to draw conclusions about, while a sample is the smaller group of individuals you’ll actually collect data from.

Defining the population

A population can be made up of anything you want to study – plants, animals, organisations, texts, countries, etc. In the social sciences, it most often refers to a group of people.

For example, will you focus on people from a specific demographic, region, or background? Are you interested in people with a certain job or medical condition, or users of a particular product?

The more precisely you define your population, the easier it will be to gather a representative sample.

Sampling methods

Even with a narrowly defined population, it’s rarely possible to collect data from every individual. Instead, you’ll collect data from a sample.

To select a sample, there are two main approaches: probability sampling and non-probability sampling . The sampling method you use affects how confidently you can generalise your results to the population as a whole.

Probability sampling is the most statistically valid option, but it’s often difficult to achieve unless you’re dealing with a very small and accessible population.

For practical reasons, many studies use non-probability sampling, but it’s important to be aware of the limitations and carefully consider potential biases. You should always make an effort to gather a sample that’s as representative as possible of the population.

Case selection in qualitative research

In some types of qualitative designs, sampling may not be relevant.

For example, in an ethnography or a case study, your aim is to deeply understand a specific context, not to generalise to a population. Instead of sampling, you may simply aim to collect as much data as possible about the context you are studying.

In these types of design, you still have to carefully consider your choice of case or community. You should have a clear rationale for why this particular case is suitable for answering your research question.

For example, you might choose a case study that reveals an unusual or neglected aspect of your research problem, or you might choose several very similar or very different cases in order to compare them.

Data collection methods are ways of directly measuring variables and gathering information. They allow you to gain first-hand knowledge and original insights into your research problem.

You can choose just one data collection method, or use several methods in the same study.

Survey methods

Surveys allow you to collect data about opinions, behaviours, experiences, and characteristics by asking people directly. There are two main survey methods to choose from: questionnaires and interviews.

Observation methods

Observations allow you to collect data unobtrusively, observing characteristics, behaviours, or social interactions without relying on self-reporting.

Observations may be conducted in real time, taking notes as you observe, or you might make audiovisual recordings for later analysis. They can be qualitative or quantitative.

Other methods of data collection

There are many other ways you might collect data depending on your field and topic.

If you’re not sure which methods will work best for your research design, try reading some papers in your field to see what data collection methods they used.

Secondary data

If you don’t have the time or resources to collect data from the population you’re interested in, you can also choose to use secondary data that other researchers already collected – for example, datasets from government surveys or previous studies on your topic.

With this raw data, you can do your own analysis to answer new research questions that weren’t addressed by the original study.

Using secondary data can expand the scope of your research, as you may be able to access much larger and more varied samples than you could collect yourself.

However, it also means you don’t have any control over which variables to measure or how to measure them, so the conclusions you can draw may be limited.

As well as deciding on your methods, you need to plan exactly how you’ll use these methods to collect data that’s consistent, accurate, and unbiased.

Planning systematic procedures is especially important in quantitative research, where you need to precisely define your variables and ensure your measurements are reliable and valid.

Operationalisation

Some variables, like height or age, are easily measured. But often you’ll be dealing with more abstract concepts, like satisfaction, anxiety, or competence. Operationalisation means turning these fuzzy ideas into measurable indicators.

If you’re using observations , which events or actions will you count?

If you’re using surveys , which questions will you ask and what range of responses will be offered?

You may also choose to use or adapt existing materials designed to measure the concept you’re interested in – for example, questionnaires or inventories whose reliability and validity has already been established.

Reliability and validity

Reliability means your results can be consistently reproduced , while validity means that you’re actually measuring the concept you’re interested in.

For valid and reliable results, your measurement materials should be thoroughly researched and carefully designed. Plan your procedures to make sure you carry out the same steps in the same way for each participant.

If you’re developing a new questionnaire or other instrument to measure a specific concept, running a pilot study allows you to check its validity and reliability in advance.

Sampling procedures

As well as choosing an appropriate sampling method, you need a concrete plan for how you’ll actually contact and recruit your selected sample.

That means making decisions about things like:

• How many participants do you need for an adequate sample size?
• What inclusion and exclusion criteria will you use to identify eligible participants?
• How will you contact your sample – by mail, online, by phone, or in person?

If you’re using a probability sampling method, it’s important that everyone who is randomly selected actually participates in the study. How will you ensure a high response rate?

If you’re using a non-probability method, how will you avoid bias and ensure a representative sample?

Data management

It’s also important to create a data management plan for organising and storing your data.

Will you need to transcribe interviews or perform data entry for observations? You should anonymise and safeguard any sensitive data, and make sure it’s backed up regularly.

Keeping your data well organised will save time when it comes to analysing them. It can also help other researchers validate and add to your findings.

On their own, raw data can’t answer your research question. The last step of designing your research is planning how you’ll analyse the data.

Quantitative data analysis

In quantitative research, you’ll most likely use some form of statistical analysis . With statistics, you can summarise your sample data, make estimates, and test hypotheses.

Using descriptive statistics , you can summarise your sample data in terms of:

• The distribution of the data (e.g., the frequency of each score on a test)
• The central tendency of the data (e.g., the mean to describe the average score)
• The variability of the data (e.g., the standard deviation to describe how spread out the scores are)

The specific calculations you can do depend on the level of measurement of your variables.

Using inferential statistics , you can:

• Make estimates about the population based on your sample data.
• Test hypotheses about a relationship between variables.

Regression and correlation tests look for associations between two or more variables, while comparison tests (such as t tests and ANOVAs ) look for differences in the outcomes of different groups.

Your choice of statistical test depends on various aspects of your research design, including the types of variables you’re dealing with and the distribution of your data.

Qualitative data analysis

In qualitative research, your data will usually be very dense with information and ideas. Instead of summing it up in numbers, you’ll need to comb through the data in detail, interpret its meanings, identify patterns, and extract the parts that are most relevant to your research question.

Two of the most common approaches to doing this are thematic analysis and discourse analysis .

There are many other ways of analysing qualitative data depending on the aims of your research. To get a sense of potential approaches, try reading some qualitative research papers in your field.

A sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect data from in your research.

For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

Statistical sampling allows you to test a hypothesis about the characteristics of a population. There are various sampling methods you can use to ensure that your sample is representative of the population as a whole.

Operationalisation means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioural avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalise the variables that you want to measure.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

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Study/Experimental/Research Design: Much More Than Statistics

Kenneth l. knight.

Brigham Young University, Provo, UT

The purpose of study, experimental, or research design in scientific manuscripts has changed significantly over the years. It has evolved from an explanation of the design of the experiment (ie, data gathering or acquisition) to an explanation of the statistical analysis. This practice makes “Methods” sections hard to read and understand.

To clarify the difference between study design and statistical analysis, to show the advantages of a properly written study design on article comprehension, and to encourage authors to correctly describe study designs.

Description:

The role of study design is explored from the introduction of the concept by Fisher through modern-day scientists and the AMA Manual of Style . At one time, when experiments were simpler, the study design and statistical design were identical or very similar. With the complex research that is common today, which often includes manipulating variables to create new variables and the multiple (and different) analyses of a single data set, data collection is very different than statistical design. Thus, both a study design and a statistical design are necessary.

Advantages:

Scientific manuscripts will be much easier to read and comprehend. A proper experimental design serves as a road map to the study methods, helping readers to understand more clearly how the data were obtained and, therefore, assisting them in properly analyzing the results.

Study, experimental, or research design is the backbone of good research. It directs the experiment by orchestrating data collection, defines the statistical analysis of the resultant data, and guides the interpretation of the results. When properly described in the written report of the experiment, it serves as a road map to readers, 1 helping them negotiate the “Methods” section, and, thus, it improves the clarity of communication between authors and readers.

A growing trend is to equate study design with only the statistical analysis of the data. The design statement typically is placed at the end of the “Methods” section as a subsection called “Experimental Design” or as part of a subsection called “Data Analysis.” This placement, however, equates experimental design and statistical analysis, minimizing the effect of experimental design on the planning and reporting of an experiment. This linkage is inappropriate, because some of the elements of the study design that should be described at the beginning of the “Methods” section are instead placed in the “Statistical Analysis” section or, worse, are absent from the manuscript entirely.

Have you ever interrupted your reading of the “Methods” to sketch out the variables in the margins of the paper as you attempt to understand how they all fit together? Or have you jumped back and forth from the early paragraphs of the “Methods” section to the “Statistics” section to try to understand which variables were collected and when? These efforts would be unnecessary if a road map at the beginning of the “Methods” section outlined how the independent variables were related, which dependent variables were measured, and when they were measured. When they were measured is especially important if the variables used in the statistical analysis were a subset of the measured variables or were computed from measured variables (such as change scores).

The purpose of this Communications article is to clarify the purpose and placement of study design elements in an experimental manuscript. Adopting these ideas may improve your science and surely will enhance the communication of that science. These ideas will make experimental manuscripts easier to read and understand and, therefore, will allow them to become part of readers' clinical decision making.

WHAT IS A STUDY (OR EXPERIMENTAL OR RESEARCH) DESIGN?

The terms study design, experimental design, and research design are often thought to be synonymous and are sometimes used interchangeably in a single paper. Avoid doing so. Use the term that is preferred by the style manual of the journal for which you are writing. Study design is the preferred term in the AMA Manual of Style , 2 so I will use it here.

A study design is the architecture of an experimental study 3 and a description of how the study was conducted, 4 including all elements of how the data were obtained. 5 The study design should be the first subsection of the “Methods” section in an experimental manuscript (see the Table ). “Statistical Design” or, preferably, “Statistical Analysis” or “Data Analysis” should be the last subsection of the “Methods” section.

Table. Elements of a “Methods” Section

The “Study Design” subsection describes how the variables and participants interacted. It begins with a general statement of how the study was conducted (eg, crossover trials, parallel, or observational study). 2 The second element, which usually begins with the second sentence, details the number of independent variables or factors, the levels of each variable, and their names. A shorthand way of doing so is with a statement such as “A 2 × 4 × 8 factorial guided data collection.” This tells us that there were 3 independent variables (factors), with 2 levels of the first factor, 4 levels of the second factor, and 8 levels of the third factor. Following is a sentence that names the levels of each factor: for example, “The independent variables were sex (male or female), training program (eg, walking, running, weight lifting, or plyometrics), and time (2, 4, 6, 8, 10, 15, 20, or 30 weeks).” Such an approach clearly outlines for readers how the various procedures fit into the overall structure and, therefore, enhances their understanding of how the data were collected. Thus, the design statement is a road map of the methods.

The dependent (or measurement or outcome) variables are then named. Details of how they were measured are not given at this point in the manuscript but are explained later in the “Instruments” and “Procedures” subsections.

Next is a paragraph detailing who the participants were and how they were selected, placed into groups, and assigned to a particular treatment order, if the experiment was a repeated-measures design. And although not a part of the design per se, a statement about obtaining written informed consent from participants and institutional review board approval is usually included in this subsection.

The nuts and bolts of the “Methods” section follow, including such things as equipment, materials, protocols, etc. These are beyond the scope of this commentary, however, and so will not be discussed.

The last part of the “Methods” section and last part of the “Study Design” section is the “Data Analysis” subsection. It begins with an explanation of any data manipulation, such as how data were combined or how new variables (eg, ratios or differences between collected variables) were calculated. Next, readers are told of the statistical measures used to analyze the data, such as a mixed 2 × 4 × 8 analysis of variance (ANOVA) with 2 between-groups factors (sex and training program) and 1 within-groups factor (time of measurement). Researchers should state and reference the statistical package and procedure(s) within the package used to compute the statistics. (Various statistical packages perform analyses slightly differently, so it is important to know the package and specific procedure used.) This detail allows readers to judge the appropriateness of the statistical measures and the conclusions drawn from the data.

STATISTICAL DESIGN VERSUS STATISTICAL ANALYSIS

Avoid using the term statistical design . Statistical methods are only part of the overall design. The term gives too much emphasis to the statistics, which are important, but only one of many tools used in interpreting data and only part of the study design:

The most important issues in biostatistics are not expressed with statistical procedures. The issues are inherently scientific, rather than purely statistical, and relate to the architectural design of the research, not the numbers with which the data are cited and interpreted. 6

Stated another way, “The justification for the analysis lies not in the data collected but in the manner in which the data were collected.” 3 “Without the solid foundation of a good design, the edifice of statistical analysis is unsafe.” 7 (pp4–5)

The intertwining of study design and statistical analysis may have been caused (unintentionally) by R.A. Fisher, “… a genius who almost single-handedly created the foundations for modern statistical science.” 8 Most research did not involve statistics until Fisher invented the concepts and procedures of ANOVA (in 1921) 9 , 10 and experimental design (in 1935). 11 His books became standard references for scientists in many disciplines. As a result, many ANOVA books were titled Experimental Design (see, for example, Edwards 12 ), and ANOVA courses taught in psychology and education departments included the words experimental design in their course titles.

Before the widespread use of computers to analyze data, designs were much simpler, and often there was little difference between study design and statistical analysis. So combining the 2 elements did not cause serious problems. This is no longer true, however, for 3 reasons: (1) Research studies are becoming more complex, with multiple independent and dependent variables. The procedures sections of these complex studies can be difficult to understand if your only reference point is the statistical analysis and design. (2) Dependent variables are frequently measured at different times. (3) How the data were collected is often not directly correlated with the statistical design.

For example, assume the goal is to determine the strength gain in novice and experienced athletes as a result of 3 strength training programs. Rate of change in strength is not a measurable variable; rather, it is calculated from strength measurements taken at various time intervals during the training. So the study design would be a 2 × 2 × 3 factorial with independent variables of time (pretest or posttest), experience (novice or advanced), and training (isokinetic, isotonic, or isometric) and a dependent variable of strength. The statistical design , however, would be a 2 × 3 factorial with independent variables of experience (novice or advanced) and training (isokinetic, isotonic, or isometric) and a dependent variable of strength gain. Note that data were collected according to a 3-factor design but were analyzed according to a 2-factor design and that the dependent variables were different. So a single design statement, usually a statistical design statement, would not communicate which data were collected or how. Readers would be left to figure out on their own how the data were collected.

MULTIVARIATE RESEARCH AND THE NEED FOR STUDY DESIGNS

With the advent of electronic data gathering and computerized data handling and analysis, research projects have increased in complexity. Many projects involve multiple dependent variables measured at different times, and, therefore, multiple design statements may be needed for both data collection and statistical analysis. Consider, for example, a study of the effects of heat and cold on neural inhibition. The variables of H max and M max are measured 3 times each: before, immediately after, and 30 minutes after a 20-minute treatment with heat or cold. Muscle temperature might be measured each minute before, during, and after the treatment. Although the minute-by-minute data are important for graphing temperature fluctuations during the procedure, only 3 temperatures (time 0, time 20, and time 50) are used for statistical analysis. A single dependent variable H max :M max ratio is computed to illustrate neural inhibition. Again, a single statistical design statement would tell little about how the data were obtained. And in this example, separate design statements would be needed for temperature measurement and H max :M max measurements.

As stated earlier, drawing conclusions from the data depends more on how the data were measured than on how they were analyzed. 3 , 6 , 7 , 13 So a single study design statement (or multiple such statements) at the beginning of the “Methods” section acts as a road map to the study and, thus, increases scientists' and readers' comprehension of how the experiment was conducted (ie, how the data were collected). Appropriate study design statements also increase the accuracy of conclusions drawn from the study.

CONCLUSIONS

The goal of scientific writing, or any writing, for that matter, is to communicate information. Including 2 design statements or subsections in scientific papers—one to explain how the data were collected and another to explain how they were statistically analyzed—will improve the clarity of communication and bring praise from readers. To summarize:

• Purge from your thoughts and vocabulary the idea that experimental design and statistical design are synonymous.
• Study or experimental design plays a much broader role than simply defining and directing the statistical analysis of an experiment.
• A properly written study design serves as a road map to the “Methods” section of an experiment and, therefore, improves communication with the reader.
• Study design should include a description of the type of design used, each factor (and each level) involved in the experiment, and the time at which each measurement was made.
• Clarify when the variables involved in data collection and data analysis are different, such as when data analysis involves only a subset of a collected variable or a resultant variable from the mathematical manipulation of 2 or more collected variables.

Acknowledgments

Thanks to Thomas A. Cappaert, PhD, ATC, CSCS, CSE, for suggesting the link between R.A. Fisher and the melding of the concepts of research design and statistics.

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Design of experiments, published by branford mcallister on july 27, 2023 july 27, 2023.

Last Updated on: 3rd February 2024, 01:28 am

Among several quantitative research alternatives is the experimental method . Experimentation is a very rigorous technique to control the conditions during data collection. This is a requirement when the objective is to determine cause and effect. 

Experimentation is suitable for dissertations and theses, and used quite often to investigate real-world problems.

There are principles of experimentation that can be applied to all quantitative research methods—even when we are only interested in correlation between variables or simply performing comparative or descriptive analysis.

In this article, I will describe the principles of experimentation, explain when and how they are used, and discuss how experiments are planned and executed.

What is Design of Experiments?

The science of experimentation was formalized about 100 years ago in England by R. A. Fisher. The principles are captured in the term, design of experiments —often called DOE or experimental design . 

The central idea is to carefully and logically plan and execute data collection and analysis to control the factors that are hypothesized to influence a measurable outcome . The outcome or response is a numerical assessment of behavior or performance. 

Renowned statistician George Box said, “All experiments are designed experiments — some are poorly designed, some are well-designed.” 

So, the intent of experimental design is to design experiments properly so we can reliably assess the influence that the control factors have on the outcome. The techniques have been proven, mathematically, to be more effective (accurate) in identifying influential factors and their impact. And, the techniques yield the most efficient use of resources for that task.

Variables – Definitions

Response variables are the measures of performance, behavior, or attributes of a system, process, population, group, or activity. They are objective, measurable, and quantitative. They represent the result or outcome of a process. For example: academic test scores.

Control factors include conditions that might influence performance, behavior, or attributes of a process, system, or activity. They can be either controlled or measured . These might include, for example, environmental conditions (day/night, weather); operational conditions (school, curriculum).

Let’s say we wish to analyze the impact that a new arithmetic curriculum has on elementary students, compared to the curriculum currently in use. The outcome (or response) is measured using a diagnostic test (comparing it to a pre-test or a control group). So, one control factor is type of curriculum . 

But, we also postulate that two other factors, gender and school, may be influential. We plan an experiment to control the three factors: curriculum (CUR), school (SCH), and gender (GDR). Let’s say for the sake of illustrating the concepts that there are two versions of the curriculum (old and new), two schools, and two genders (male and female).

We’ll carry this example through the article.

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Factorial Experiments 

The purest form of a controlled, designed experiment is the factorial experiment .

A factorial experiment varies all of the control factors together instead of one at a time or some other scheme. A full factorial design investigates all combinations of factor levels. 

Factorial designs provide the most efficient and effective method of assessing the influence of control factors across the entire factor space. The influence is assessed using analysis of variance (ANOVA).

In our example, the experiment has three control factors (CUR, SCH, and GDR), at two levels each. The matrix of control factors and their levels is illustrated in this table:

We use here a form of coding called effects coding . We represent two-level factors with +1 and -1. When there are factors with more levels, effects coding can employ other numbers, as long as the codes for any factor sum to zero. We will save the discussion on factor coding for another article.

We can see that in our experiment, there are 2 x 2 x 2 = 2 3 = 8 combinations of factor levels. The table represents those combinations as 8 cases .

It is likely that we would need more sample size than 8. Sample size enables the following:

• Adequate precision (effect size).
• Adequate statistical power (the inverse of the probability of a Type II or false negative statistical error).
• Adequate statistical confidence (the inverse of the probability of a Type I or false positive statistical error).

To get more sample size, we simply replicate (i.e., repeat) the cases. That is, we sample multiples of each case as shown here (replication of 2):

The sample size needed, and hence the replication of cases, is computed using an app such as G*Power (Faul et al. 2009). In this example, we have 8 cases, replicated twice, for a sample size of 16.

Fractional Factorial Designs

Sometimes it is not possible to run all possible combinations of factor levels (perhaps insufficient resources to execute a full factorial with replication). As an alternative, we can use a mathematically derived subset of the entire set of combinations of the full factorial, called a fractional factorial . 

For example, if instead of our full factorial, we employ a logically derived subset of the original 8 cases as highlighted here, and replicate these 4 cases (a half fractional factorial ):

The cases are chosen by aliasing or confounding a two-factor interaction (SCH*GDR) with the control factor, CUR. The assumption is that the two-factor interaction SCH*GDR is not meaningful. So, the interaction is confounded with CUR and its effects are not distinguishable from the effects of CUR. 

With proper sample size, a fractional factorial is capable of identifying significant main effects and interactions.

Major Principles of Experimental Design

The major principles of experimental design include the following: 

• Quantitative, measurable response variables—outputs of a process or system.
• Precision when measuring response variables.
• Control factors and independent variables—inputs to a process or system.
• A real-world process tested with an instrument (a test, observation, or simulation experiment using a model of the real system or process).
• Designed experiments—controlling the factors and measuring the associated variation in the response variables.
• Factorial or fractional factorial designs—assessing all combinations/cases.
• Orthogonality among levels of the control factors.
• Power analysis (sample size calculations based on effect size, statistical confidence, and statistical power).
• Replication of cases to achieve minimum required sample size.
• Random selection of cases (combinations of control factors and their levels).

Even in quasi- or non-experimental designs, many of these principles can and should be applied when planning and conducting research and analysis. For example, a non-experimental comparative study using a questionnaire should incorporate these attributes:

• A quantitative, measurable response variable informed by the average score on a subset of the questions.
• A control over the participant demographics achieved with stratified sampling.
• A factorial design assessing all combinations of demographics (cases).
• Power analysis (calculating sample size based on effect size, confidence, and power).
• Random selection of cases within each stratum.

What Experimental Design Contributes

Experimental design was developed to assess the influence that predictors have on response variables (system outputs). That is, to facilitate a mathematically rigorous assessment of how a change in inputs results in a corresponding change in outputs .

The essential idea behind a designed experiment is control—to purposefully manipulate the values or levels of the control factors in order to measure the corresponding change in response variables. This is done in a way that mathematically associates the change in system performance within controlled, measurable conditions. 

In some analyses, it may be desirable or necessary to allow some predictors to vary, randomly, within a range; instead of setting fixed values. In this case, though there is an impact on statistical power and confidence, at the very least these control factors are measured as precisely as possible so that their variation can be associated with variation in the response variable. In this situation, multiple linear regression is the analysis tool.

Experimental design permits us to accomplish these objectives reliably:

• Characterize the sensitivity of response variables to changes in the predictors.
• Determine which predictors are clearly influential.
• Identify which predictors are clearly not significant, then reduce the number of cases to analyze.
• Identify interactions between control factors.
• Identify factors that are not significant individually, but moderators of other predictors.
• Predict system performance or behavior.
• Identify key cases for subject matter expert interpretation.
• Use the same control factors and common response variables during separate analyses and using different research designs and methods.
• Combine or compare performance and behavior across research designs and methods.

Experimental Design and Analysis Considerations

Any experiment or analysis should be planned to address a research problem, purpose, and research question. Planning should not only respond to the fundamental objectives of the research, but also account for resource limitations, such as

• Capacity (for example, human effort and computer resources).
• Competing demands for the resources (money).

Therefore, it is essential to 

• Prioritize the use of scarce resources.
• Use efficient methodologies (experimental designs and analytical methods).
• Seek no more precision than is needed to answer a question or meet an analytical objective. 

An experimental design and analytical method are chosen that, within the resource constraints, offer the greatest potential to address the analytical objective that motivated the experiment. There will be tradeoffs among competing attributes of various designs (e.g., trading statistical precision against sample size). 

The following are some considerations for choosing a design that answers questions adequately, maximizes efficiency, and makes appropriate tradeoffs in experimental attributes.

Sequential Experimentation

Sequential experimentation involves a linked series of experiments:

• Building on what is learned through analysis in the previous experiment.
• Refining understanding of the system or process—the significant and non-significant explanatory factors. 
• Reducing factor space based on analysis-based factor screening —smaller, more focused, more efficient follow-on experiments.
• Refining and re-focusing analytical objectives, methodologies, and statistical tests.
• Investigating specific cases where performance or behavior is unexpected or interesting.
• Using data previously collected and analyzed to inform future experiments.
• Computing variance in response variables that aids in performing sample size calculations for subsequent experiments.

Orthogonality

In an orthogonal design (as in a factorial experiment), the main effect of each control factor can be estimated independently without confounding the effect of one control factor by another. 

In other words, the estimated effect of one control factor will not interfere with the estimated effect of another control factor. 

The importance of orthogonal designs is their capability to minimize the effects of collinearity . A confident estimate of control factor effects leads to understanding the true system performance.

Factor Interactions

Factorial designs enable the experimenter to investigate not only the individual effects (or influence) of each control factor (main effects) but the interaction of control factors with each other. 

A two-factor interaction means this: The effect that a control factor has on the response depends on the value of a second control factor. For example . . . the influence of one predictor (say, CUR) on the response (Y = test scores) depends on the value of another predictor (say, SCH). The relationship between CUR and Y (the slope or coefficient) changes depending on the value of SCH.

A two-factor interaction represents a qualification on any claim that one control factor influences the response. Some of the most important insights are gleaned from two-factor interactions.

A two-factor interaction is calculated as the product of its two control factors, as shown in this table:

Two-factor interactions are evaluated in ANOVA just as if they were individual predictors.

The conclusions about the significance and magnitude of relationships between control factors and the response variable must include a discussion of the significant two-factor interactions.

Factor Aliasing

Aliasing in a test matrix occurs when the levels for a control factor are correlated with another control factor. This causes the main effects (influence of individual control factors) to be confounded (i.e., the effects cannot be estimated separately from one another). 

The alias structure of an experiment matrix characterizes the confounding within the experimental design and can be evaluated using software applications (e.g., SPSS). The alias matrix describes the degree to which the control factors are confounded with one another. A rule of thumb in complex designs is that control factors whose aliasing is less than |0.7| can be evaluated in the model. If the aliasing is greater than |0.7|, one of the control factors should be considered for removal from the analysis; or the control factors should be combined.

Factorial designs avoid problems with factor aliasing. The issue is most prevalent in fractional factorials.

Pseudo-factorial Designs

ANOVA and factorial designs go hand in hand because the predictors (control factors) are categorical variables, suitable for controlling and readily analyzed using ANOVA. The advantage of a factorial design is that it is capable, with high power and confidence, of detecting the influence of control factors on the response, with an efficient use of resources. Another advantage is the ability to calculate and evaluate interactions between control factors. 

There are some disadvantages of factorial designs:

• Nonlinearities between the points defined by the control factor levels may not be detected
• The control factor levels may be set at a relatively small number of discrete points. 
• The design may not provide a detailed understanding of performance throughout the factor space (i.e., between points). 
• Some control factors may not be controllable (e.g., air temperature and pressure).

In these kinds of experiments, ANOVA and pure factorial experiments may not be the best option. 

An alternative is a pseudo-factorial experiment . This approach allows some latitude in the values of some of the predictors, while preserving some of the principles of factorial experiments. These designs are built around a factorial experiment in which the quantitative predictors are allowed to vary randomly within an operational range. Those ranges are controlled as if they were categorical. 

Final Thoughts

An experiment is a powerful research design for assessing the influence of factors on the performance or behavior of systems, activities, and other phenomena. Proper experimental design is essential when assessing cause and effect. But, the principles of experimental design are also desirable attributes in many if not most quantitative research and analysis.

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Branford McAllister

Branford McAllister received his PhD from Walden University in 2005. He has been an instructor and PhD mentor for the University of Phoenix, Baker College, and Walden University; and a professor and lecturer on military strategy and operations at the National Defense University. He has technical and management experience in the military and private sector, has research interests related to leadership, and is an expert in advanced quantitative analysis techniques. He is passionately committed to mentoring students in post-secondary educational programs. Book a Free Consultation with Branford McAllister

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This chapter provides an overview of the econometric and statistical methods for drawing inference on causal effects from randomized experiments under the potential outcome approach. Well-designed and conducted randomized experiments are generally considered to be the gold standard for obtaining objective causal inferences, but the design and analysis of experiments require to address a number of statistical issues. This chapter first discusses design and inferential issues in classical randomized experiments, by providing insights on the relative advantages and drawbacks of alternative types of classical randomized experiments. Then, it discusses complications arising from clustered randomization, multiple site experiments, and rerandomization as well as issues arising in the design and analysis of randomized experiments with posttreatment complications, sequential and dynamic experiments, and experiments in settings with interference. Recently developed approaches for estimating causal effects using machine learning methods are also described. This chapter concludes with some discussion on the external and internal validity of randomized experiments.

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Acknowledgments

Responsible Section Editor: Alfonso Flores-Lagunes. The chapter has benefited from valuable comments of the editors and anonymous referees. The chapter was supported by the Department of Statistics, Computer Science, Applications of the University of Florence, (authors’ affiliation) through funding received as Department of Excellence 2018-2022 from the Italian Ministry of Education, University and Research (MIUR). There is no conflict of interest.

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Mattei, A., Mealli, F., Nodehi, A. (2021). Design and Analysis of Experiments. In: Zimmermann, K.F. (eds) Handbook of Labor, Human Resources and Population Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-57365-6_40-1

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DOI : https://doi.org/10.1007/978-3-319-57365-6_40-1

Received : 02 August 2021

Accepted : 04 August 2021

Published : 12 January 2022

Publisher Name : Springer, Cham

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• GETTING STARTED
• Introduction
• FUNDAMENTALS

Getting to the main article

Choosing your route

Setting research questions/ hypotheses

Assessment point

Building the theoretical case

Setting your research strategy

Data collection

Data analysis

Research design

The quantitative research design that you set in your dissertation should reflect the type of research questions/hypotheses that you have set. When we talk about quantitative research designs, we are typically referring to research following either a descriptive , experimental , quasi-experimental and relationship-based research design, which we will return to shortly. However, there are also specific goals that you may want to achieve within these research designs. You may want to: (Goal A) explore whether there is a relationship between different variables; (Goal B) predict a score or a membership of a group; or (Goal C) find out the differences between groups you are interested in or treatment conditions that you want to investigate:

GOAL A Exploring the relationship between variables

Are you trying to determine if there is a relationship between two or more variables, and what this relationship is? This kind of design is used to answer questions such as: Is there a relationship between height and basketball performance? Are males more likely to be smokers than females? Does you level of anxiety reduce your exam ability?

GOAL B Predicting a score or a membership of a group

Are you trying to examine whether one variable's value (i.e., the dependent or outcome variable) can be predicted based on another's (i.e., the independent variable). These designs answer questions such as: Can I predict 10km run time based on an individual's aerobic capacity? Can I predict exam anxiety based on knowing the number of hours spent revising? Can I predict whether someone is classified as computer literate based on their performance in different computer tasks? Can I predict an individual's preferred transport (car/motorcycle) based on their response to a risk questionnaire?

GOAL C Testing for differences between groups or treatment conditions

Are you trying to test for differences between groups (e.g., exam performance of males and females) or treatment conditions (e.g., employee turnover among employees (a) given a bonus and (b) not given a bonus)? This type of design aims to answer questions such as: What is the difference in jump height between males and females? Can an exercise-training programme lead to a reduction in blood sugar levels? Do stressed males and females respond differently to different stress-reduction therapies? In each of these cases, we have different groups that we are comparing (e.g., males versus females), and we may also have different treatments (e.g., the example of multiple stress-reduction therapies).

Goals A and B reflect the use of relationship-based research questions/hypotheses, whilst goal C reflects the use of comparative research questions/hypotheses. Just remember that in addition to relating and comparing (i.e., relationship-based and comparative research questions/hypotheses), quantitative research can also be used to describe the phenomena we are interested in (i.e., descriptive research questions). These three basic approaches (i.e., describing , relating and comparing ) can be seen in the following example:

Let's imagine we are interested in examining Facebook usage amongst university students in the United States .

We could describe factors relating to the make-up of these Facebook users, quantifying how many (or what proportion) of these university students were male or female, or what their average age was. We could describe factors relating to their behaviour, such as how frequently they used Facebook each week or the reasons why they joined Facebook in the first place (e.g., to connect with friends, to store all their photos in one place, etc.).

We could compare some of these factors (i.e., those factors that we had just described). For example, we could compare how frequently the students used Facebook each week, looking for differences between male and female students.

We could relate one or more of these factors (e.g., age) to other factors we had examined (e.g., how frequently students used Facebook each week) to find out if there were any associations or relationships between them. For example, we could relate age to how frequently the students used Facebook each week. This could help us discover if there was an association or relationship between these variables (i.e., age and weekly Facebook usage), and if so, tell us something about this association or relationship (e.g., its strength, direction, and/or statistical significance).

These three approaches to examining the constructs you are interested in (i.e., describing , comparing and relating ) are addressed by setting descriptive research questions, and/or comparative or relationship-based research questions/hypotheses. By this stage, you should be very clear about the type of research questions/hypotheses you are addressing, but if you are unsure, refer back to the Research Questions & Hypotheses section of the Fundamentals part of Lærd Dissertation now.

If you are exploring the relationship between variables (i.e., Goal A ), you are likely to be following a relationship-based research design (i.e., a type of non-experimental research design). However, if you are predicting the score or a membership of a group (i.e., Goal B ) or testing for differences between groups or treatment conditions (i.e., Goal C ), you are likely to be following either an experimental or quasi-experimental research design. Unless you already understand the differences between experimental, quasi-experimental and relationship-based research designs, you should read about these different research designs in the Research Designs section of the Fundamentals part of Lærd Dissertation now. You need to do this for two main reasons:

You will have to state which type of research design you are using in your dissertation when writing up the Research Design section of your Chapter Three: Research Strategy .

The research design that you use has a significant influence on your choice of research methods , the research quality of your findings, and even aspects of research ethics that you will have to think about.

Once you are familiar with the four types of research design (i.e., descriptive, experimental, quasi-experimental and relationship-based), you need to think about the route that you are adopting, and the approach within that route in order to set the research design in your dissertation:

• ROUTE A: Duplication
• ROUTE B: Generalisation
• ROUTE C: Extension

Route A: Duplication

If you are taking on Route A: Duplication , you would typically not be expected to make any changes to the research design used in the main journal article when setting the research design for your dissertation. After all, the purpose of the dissertation is duplication , where you are, in effect, re-testing the study in the main journal article to see if the same (or similar) findings are found. An important aspect of such re-testing is typically the use of the same research strategy applied in the main journal article. As such, if an experimental research design was used in the main journal article, with 3 groups (e.g., two treatment groups and one control group), your dissertation would also use an experimental design with the same group characteristics (i.e., 3 groups, with two treatment groups and one control group). The research design you used would also have the same goals as those in the main journal article (e.g., the goal of relating two constructs, perhaps study time and exam performance, in order to answer a relationship-based research question/hypothesis).

However, there are some instances where, from a practical standpoint, you may find that it is not possible to use the same research design, perhaps because an experimental research design was used, but you are unable to randomly selected people from the population you can get access to, forcing you to use a quasi-experimenta l research design. But the goal will be to use the same research design in your dissertation as the one applied in the main journal article. Again, you can learn about the differences between experimental and quasi-experimental designs in the Research Designs section of the Fundamentals part of Lærd Dissertation.

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Guerreiro, Luís Filipe Costa. "Automatic drilling improvement and standardization by design-of-experiments (DOE)." Master's thesis, Universidade de Évora, 2019. http://hdl.handle.net/10174/25737.

Choi, Paul Koon Ping. "The use of design of experiments (DOE) : time for company management to decide." Thesis, University of the West of Scotland, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.556176.

Khaddaj-Mallat, Chadi. "Design of experiments approach to the flooding of damaged ships." Ecole centrale de Nantes, 2010. http://www.theses.fr/2010ECDN0024.

Johansson, Robin. "Structural optimization of electronic packages using DOE." Thesis, KTH, Hållfasthetslära, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-285859.

Verlaan, Eric, Wouter Hendriksen, Rob Meulenbroek, and Prie Devlin du. "Design of Experiments (DOE) for Product and Process Improvements - 130: A Phenolic Syntan Case Study." Verein für Gerberei-Chemie und -Technik e. V, 2019. https://slub.qucosa.de/id/qucosa%3A34176.

Chini, Marco. "Sviluppo di nuove metodologie di calibrazione per motori da competizione con tecniche di Design of Experiments." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18647/.

Lindberg, Tomas. "An application of DOE in the evaluation of optimization functions in a statistical software." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-39507.

Chantarat, Navara. "Modern design of experiments methods for screening and experimentations with mixture and qualitative variables." Columbus, OH : Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1064198056.

Farias, Marcelo Fernandes. "Determinação da influência de parâmetros de processo de forjamento a quente utilizando DOE (projeto de experimentos)." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2017. http://hdl.handle.net/10183/170979.

Clay, Stephen Brett. "Characterization of Crazing Properties of Polycarbonate." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/28648.

Sandqvist, Wedin Emma. "Optimization of Acidic Degradation of Hyaluronic Acid using Design of Experiments." Thesis, Linköpings universitet, Teknisk biologi, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-156273.

Smeliková, Lenka. "Kontrola kvality pájeného spoje a Design of Experiments u strojního pájení vlnou." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2014. http://www.nusl.cz/ntk/nusl-220991.

Amanna, Ashwin Earl. "Statistical Experimental Design Framework for Cognitive Radio." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/77331.

Henriques, Francisco José da Silva. "O uso do DOE em conjunto com FTA no desenvolvimento e melhoria de projetos inovadores." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263938.

Westbeld, Julius. "Investigation of support structures of a polymer powder bed fusion process by use of Design of Experiment (DoE)." Thesis, KTH, Lättkonstruktioner, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-243867.

Scheffler, Liziane da Luz Seben. "Estudo exploratório de extração de celulose a partir de resíduos vegetais do processo produtivo de conserva de palmito (Archontophoenix alexandrae)." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2011. http://hdl.handle.net/10183/35616.

Sabová, Iveta. "Plánovaný experiment." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-231981.

Nilsson, Marcus, and Johan Ruth. "SPC and DOE in production of organic electronics." Thesis, Linköping University, Department of Science and Technology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-6240.

At Acreo AB located in Norrköping, Sweden, research and development in the field of organic electronics have been conducted since 1998. Several electronic devices and systems have been realized. In late 2003 a commercial printing press was installed to test large scale production of these devices. Prior to the summer of 2005 the project made significant progress. As a step towards industrialisation, the variability and yield of the printing process needed to bee studied. A decision to implement Statistical Process Control (SPC) and Design of Experiments (DOE) to evaluate and improve the process was taken.

SPC has been implemented on the EC-patterning step in the process. A total of 26 Samples were taken during the period October-December 2005. An - and s-chart were constructed from these samples. The charts clearly show that the process is not in statistical control. Investigations of what causes the variation in the process have been performed. The following root causes to variation has been found:

PEDOT:PSS-substrate sheet resistance and poorly cleaned screen printing drums.

After removing points affected by root causes, the process is still not in control. Further investigations are needed to get the process in control. Examples of where to go next is presented in the report. In the DOE part a four factor full factorial experiment was performed. The goal with the experiment was to find how different factors affects switch time and life length of an electrochromic display. The four factors investigated were: Electrolyte, Additive, Web speed and Encapsulation. All statistical analysis was performed using Minitab 14. The analysis of measurements from one day and seven days after printing showed that:

- Changing Electrolyte from E230 to E235 has small effect on the switch time

- Adding additives Add1 and Add2 decreases the switch time after 1 and 7 days

- Increasing web speed decreases the switch time after 1 and 7 days

- Encapsulation before UV-step decreases the switch time after 7 days

Rådberg, Malin. "Design of Experiment for Laser cutting in Superalloy Haynes 282." Thesis, Karlstads universitet, Science, Mathematics and Engineering Education Research (SMEER), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-44516.

Nelson, Benjamin D. "Using Design of Experiments and Electron Backscatter Diffraction to Model Extended Plasticity Mechanisms In Friction Stir Welded AISI 304L Stainless Steel." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2582.

Knob, Jan. "Pěnění fermentačních zbytků při vakuovém odpařování." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-378403.

Andersson, David. "Multivariate design of molecular docking experiments : An investigation of protein-ligand interactions." Doctoral thesis, Umeå universitet, Kemiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-35736.

Bredda, Eduardo Henrique. "Estudo comparativo e otimização da quantidade de ômega 3 e ômega 6 produzido pelas microalgas nannochloropsis gaditana e dunaliella salina /." Guaratinguetá, 2019. http://hdl.handle.net/11449/183502.

Tosto, Francesco. "Investigation of performance and surge behavior of centrifugal compressors through CFD simulations." Thesis, KTH, Mekanik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-226159.

Hizli, Cem. "Thermal Optimization of Veo+ Projectors (thesis work at Optea AB) : Trying to reduce noise of the Veo+ projector by DOE (Design of Experiment) tests to find anoptimal solution for the fan algorithm while considering the thermal specifics of the unit." Thesis, Mälardalens högskola, Akademin för innovation, design och teknik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-10382.

Holec, Tomáš. "Plánovaný experiment." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2016. http://www.nusl.cz/ntk/nusl-254455.

Venturini, Giacomo. "Design of experiment analysis of air filter performance for helicopter applications." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.

Jakob, Marius. "Methode zur Gestaltung anwendungsabhängiger Mitnehmerverbindungen: Leichtbau und Steigerung der Tragfähigkeit durch dünnwandige Profilwellen." Technische Universität Chemnitz, 2019. https://monarch.qucosa.de/id/qucosa%3A34105.

Fogliatto, Aloysio Arthur Becker. "Influência dos parâmetros do processo MIG/MAG com curto-circuito controlado sobre a geometria do cordão de solda." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/75921.

Borunský, Tomáš. "Optimalizace procesu tlakového lití VN přístrojových transformátorů." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228552.

Laiate, Juliana. "Estudo do processo de cultivo da microalga chlorella minutíssima e caracterização termoquímica de sua biomassa para aplicação em gaseificação." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/157246.

Zavoli, Chiara. "Applicazione del metodo Design of Experiment per l’analisi del ciclo di decontaminazione con H2O2 nell’industria farmaceutica." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

Haase, Dirk. "Ein neues Verfahren zur modellbasierten Prozessoptimierung auf der Grundlage der statistischen Versuchsplanung am Beispiel eines Ottomotors mit elektromagnetischer Ventilsteuerung (EMVS)." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2005. http://nbn-resolving.de/urn:nbn:de:swb:14-1129553378853-30864.

Yurtseven, Saygin. "Analysis Of The Influence Of Non-machining Process Parameters On Product Quality By Experimental Design And Statistical Analysis." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1026863/index.pdf.

Nwagoum, Idriss Chatrian. "aerodynamic performance improvement of a twin scroll turbocharger turbine using the design of experiments method." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.

Panieri, Marco. "Ottimizzazione mediante progetto dell'esperimento del processo di produzione di idrossiapatite drogata con magnesio." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017.

Abdalrahman, Rzgar. "Design and analysis of integrally-heated tooling for polymer composites." Thesis, University of Plymouth, 2015. http://hdl.handle.net/10026.1/4753.

Fukuda, Isa Martins. "Desenvolvimento e otimização de protetores solares empregando os conceitos de qualidade por design (QbD) e tecnologia analí­tica de processos (PAT)." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/9/9139/tde-12112018-145821/.

Haase, Dirk. "Ein neues Verfahren zur modellbasierten Prozessoptimierung auf der Grundlage der statistischen Versuchsplanung am Beispiel eines Ottomotors mit elektromagnetischer Ventilsteuerung (EMVS)." Doctoral thesis, Technische Universität Dresden, 2004. https://tud.qucosa.de/id/qucosa%3A24582.

Berglund, Anders. "Criteria for Machinability Evaluation of Compacted Graphite Iron Materials : Design and Production Planning Perspective on Cylinder Block Manufacturing." Doctoral thesis, KTH, Industriell produktion, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-48430.

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Abbas, Manzar. "System-level health assessment of complex engineered processes." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37260.

Besirevic, Edin, and Anders Dahl. "Variance reduction of product parameters in wire rope production by optimisation of process parameters." Thesis, Luleå tekniska universitet, Institutionen för ekonomi, teknik och samhälle, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-63634.

BATISTA, NETO Leopoldo Viana. "Otimização do processo de disposição de filmes TiN e TiZrN em aço inoxidável utilizando planejamento experimental fatorial." Universidade Federal de Campina Grande, 2014. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/378.

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Experimental Research Design — 6 mistakes you should never make!

Since school days’ students perform scientific experiments that provide results that define and prove the laws and theorems in science. These experiments are laid on a strong foundation of experimental research designs.

An experimental research design helps researchers execute their research objectives with more clarity and transparency.

In this article, we will not only discuss the key aspects of experimental research designs but also the issues to avoid and problems to resolve while designing your research study.

Table of Contents

What Is Experimental Research Design?

Experimental research design is a framework of protocols and procedures created to conduct experimental research with a scientific approach using two sets of variables. Herein, the first set of variables acts as a constant, used to measure the differences of the second set. The best example of experimental research methods is quantitative research .

Experimental research helps a researcher gather the necessary data for making better research decisions and determining the facts of a research study.

When Can a Researcher Conduct Experimental Research?

A researcher can conduct experimental research in the following situations —

• When time is an important factor in establishing a relationship between the cause and effect.
• When there is an invariable or never-changing behavior between the cause and effect.
• Finally, when the researcher wishes to understand the importance of the cause and effect.

Importance of Experimental Research Design

To publish significant results, choosing a quality research design forms the foundation to build the research study. Moreover, effective research design helps establish quality decision-making procedures, structures the research to lead to easier data analysis, and addresses the main research question. Therefore, it is essential to cater undivided attention and time to create an experimental research design before beginning the practical experiment.

By creating a research design, a researcher is also giving oneself time to organize the research, set up relevant boundaries for the study, and increase the reliability of the results. Through all these efforts, one could also avoid inconclusive results. If any part of the research design is flawed, it will reflect on the quality of the results derived.

Types of Experimental Research Designs

Based on the methods used to collect data in experimental studies, the experimental research designs are of three primary types:

1. Pre-experimental Research Design

A research study could conduct pre-experimental research design when a group or many groups are under observation after implementing factors of cause and effect of the research. The pre-experimental design will help researchers understand whether further investigation is necessary for the groups under observation.

Pre-experimental research is of three types —

• One-shot Case Study Research Design
• One-group Pretest-posttest Research Design
• Static-group Comparison

2. True Experimental Research Design

A true experimental research design relies on statistical analysis to prove or disprove a researcher’s hypothesis. It is one of the most accurate forms of research because it provides specific scientific evidence. Furthermore, out of all the types of experimental designs, only a true experimental design can establish a cause-effect relationship within a group. However, in a true experiment, a researcher must satisfy these three factors —

• There is a control group that is not subjected to changes and an experimental group that will experience the changed variables
• A variable that can be manipulated by the researcher
• Random distribution of the variables

This type of experimental research is commonly observed in the physical sciences.

3. Quasi-experimental Research Design

The word “Quasi” means similarity. A quasi-experimental design is similar to a true experimental design. However, the difference between the two is the assignment of the control group. In this research design, an independent variable is manipulated, but the participants of a group are not randomly assigned. This type of research design is used in field settings where random assignment is either irrelevant or not required.

The classification of the research subjects, conditions, or groups determines the type of research design to be used.

Advantages of Experimental Research

Experimental research allows you to test your idea in a controlled environment before taking the research to clinical trials. Moreover, it provides the best method to test your theory because of the following advantages:

• Researchers have firm control over variables to obtain results.
• The subject does not impact the effectiveness of experimental research. Anyone can implement it for research purposes.
• The results are specific.
• Post results analysis, research findings from the same dataset can be repurposed for similar research ideas.
• Researchers can identify the cause and effect of the hypothesis and further analyze this relationship to determine in-depth ideas.
• Experimental research makes an ideal starting point. The collected data could be used as a foundation to build new research ideas for further studies.

6 Mistakes to Avoid While Designing Your Research

There is no order to this list, and any one of these issues can seriously compromise the quality of your research. You could refer to the list as a checklist of what to avoid while designing your research.

1. Invalid Theoretical Framework

Usually, researchers miss out on checking if their hypothesis is logical to be tested. If your research design does not have basic assumptions or postulates, then it is fundamentally flawed and you need to rework on your research framework.

2. Inadequate Literature Study

Without a comprehensive research literature review , it is difficult to identify and fill the knowledge and information gaps. Furthermore, you need to clearly state how your research will contribute to the research field, either by adding value to the pertinent literature or challenging previous findings and assumptions.

3. Insufficient or Incorrect Statistical Analysis

Statistical results are one of the most trusted scientific evidence. The ultimate goal of a research experiment is to gain valid and sustainable evidence. Therefore, incorrect statistical analysis could affect the quality of any quantitative research.

4. Undefined Research Problem

This is one of the most basic aspects of research design. The research problem statement must be clear and to do that, you must set the framework for the development of research questions that address the core problems.

5. Research Limitations

Every study has some type of limitations . You should anticipate and incorporate those limitations into your conclusion, as well as the basic research design. Include a statement in your manuscript about any perceived limitations, and how you considered them while designing your experiment and drawing the conclusion.

6. Ethical Implications

The most important yet less talked about topic is the ethical issue. Your research design must include ways to minimize any risk for your participants and also address the research problem or question at hand. If you cannot manage the ethical norms along with your research study, your research objectives and validity could be questioned.

Experimental Research Design Example

In an experimental design, a researcher gathers plant samples and then randomly assigns half the samples to photosynthesize in sunlight and the other half to be kept in a dark box without sunlight, while controlling all the other variables (nutrients, water, soil, etc.)

By comparing their outcomes in biochemical tests, the researcher can confirm that the changes in the plants were due to the sunlight and not the other variables.

Experimental research is often the final form of a study conducted in the research process which is considered to provide conclusive and specific results. But it is not meant for every research. It involves a lot of resources, time, and money and is not easy to conduct, unless a foundation of research is built. Yet it is widely used in research institutes and commercial industries, for its most conclusive results in the scientific approach.

Have you worked on research designs? How was your experience creating an experimental design? What difficulties did you face? Do write to us or comment below and share your insights on experimental research designs!

Frequently Asked Questions

Randomization is important in an experimental research because it ensures unbiased results of the experiment. It also measures the cause-effect relationship on a particular group of interest.

Experimental research design lay the foundation of a research and structures the research to establish quality decision making process.

There are 3 types of experimental research designs. These are pre-experimental research design, true experimental research design, and quasi experimental research design.

The difference between an experimental and a quasi-experimental design are: 1. The assignment of the control group in quasi experimental research is non-random, unlike true experimental design, which is randomly assigned. 2. Experimental research group always has a control group; on the other hand, it may not be always present in quasi experimental research.

Experimental research establishes a cause-effect relationship by testing a theory or hypothesis using experimental groups or control variables. In contrast, descriptive research describes a study or a topic by defining the variables under it and answering the questions related to the same.

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Home » Experimental Design – Types, Methods, Guide

Experimental Design – Types, Methods, Guide

Table of Contents

Experimental Design

Experimental design is a process of planning and conducting scientific experiments to investigate a hypothesis or research question. It involves carefully designing an experiment that can test the hypothesis, and controlling for other variables that may influence the results.

Experimental design typically includes identifying the variables that will be manipulated or measured, defining the sample or population to be studied, selecting an appropriate method of sampling, choosing a method for data collection and analysis, and determining the appropriate statistical tests to use.

Types of Experimental Design

Here are the different types of experimental design:

Completely Randomized Design

In this design, participants are randomly assigned to one of two or more groups, and each group is exposed to a different treatment or condition.

Randomized Block Design

This design involves dividing participants into blocks based on a specific characteristic, such as age or gender, and then randomly assigning participants within each block to one of two or more treatment groups.

Factorial Design

In a factorial design, participants are randomly assigned to one of several groups, each of which receives a different combination of two or more independent variables.

Repeated Measures Design

In this design, each participant is exposed to all of the different treatments or conditions, either in a random order or in a predetermined order.

Crossover Design

This design involves randomly assigning participants to one of two or more treatment groups, with each group receiving one treatment during the first phase of the study and then switching to a different treatment during the second phase.

Split-plot Design

In this design, the researcher manipulates one or more variables at different levels and uses a randomized block design to control for other variables.

Nested Design

This design involves grouping participants within larger units, such as schools or households, and then randomly assigning these units to different treatment groups.

Laboratory Experiment

Laboratory experiments are conducted under controlled conditions, which allows for greater precision and accuracy. However, because laboratory conditions are not always representative of real-world conditions, the results of these experiments may not be generalizable to the population at large.

Field Experiment

Field experiments are conducted in naturalistic settings and allow for more realistic observations. However, because field experiments are not as controlled as laboratory experiments, they may be subject to more sources of error.

Experimental Design Methods

Experimental design methods refer to the techniques and procedures used to design and conduct experiments in scientific research. Here are some common experimental design methods:

Randomization

This involves randomly assigning participants to different groups or treatments to ensure that any observed differences between groups are due to the treatment and not to other factors.

Control Group

The use of a control group is an important experimental design method that involves having a group of participants that do not receive the treatment or intervention being studied. The control group is used as a baseline to compare the effects of the treatment group.

Blinding involves keeping participants, researchers, or both unaware of which treatment group participants are in, in order to reduce the risk of bias in the results.

Counterbalancing

This involves systematically varying the order in which participants receive treatments or interventions in order to control for order effects.

Replication

Replication involves conducting the same experiment with different samples or under different conditions to increase the reliability and validity of the results.

This experimental design method involves manipulating multiple independent variables simultaneously to investigate their combined effects on the dependent variable.

This involves dividing participants into subgroups or blocks based on specific characteristics, such as age or gender, in order to reduce the risk of confounding variables.

Data Collection Method

Experimental design data collection methods are techniques and procedures used to collect data in experimental research. Here are some common experimental design data collection methods:

Direct Observation

This method involves observing and recording the behavior or phenomenon of interest in real time. It may involve the use of structured or unstructured observation, and may be conducted in a laboratory or naturalistic setting.

Self-report Measures

Self-report measures involve asking participants to report their thoughts, feelings, or behaviors using questionnaires, surveys, or interviews. These measures may be administered in person or online.

Behavioral Measures

Behavioral measures involve measuring participants’ behavior directly, such as through reaction time tasks or performance tests. These measures may be administered using specialized equipment or software.

Physiological Measures

Physiological measures involve measuring participants’ physiological responses, such as heart rate, blood pressure, or brain activity, using specialized equipment. These measures may be invasive or non-invasive, and may be administered in a laboratory or clinical setting.

Archival Data

Archival data involves using existing records or data, such as medical records, administrative records, or historical documents, as a source of information. These data may be collected from public or private sources.

Computerized Measures

Computerized measures involve using software or computer programs to collect data on participants’ behavior or responses. These measures may include reaction time tasks, cognitive tests, or other types of computer-based assessments.

Video Recording

Video recording involves recording participants’ behavior or interactions using cameras or other recording equipment. This method can be used to capture detailed information about participants’ behavior or to analyze social interactions.

Data Analysis Method

Experimental design data analysis methods refer to the statistical techniques and procedures used to analyze data collected in experimental research. Here are some common experimental design data analysis methods:

Descriptive Statistics

Descriptive statistics are used to summarize and describe the data collected in the study. This includes measures such as mean, median, mode, range, and standard deviation.

Inferential Statistics

Inferential statistics are used to make inferences or generalizations about a larger population based on the data collected in the study. This includes hypothesis testing and estimation.

Analysis of Variance (ANOVA)

ANOVA is a statistical technique used to compare means across two or more groups in order to determine whether there are significant differences between the groups. There are several types of ANOVA, including one-way ANOVA, two-way ANOVA, and repeated measures ANOVA.

Regression Analysis

Regression analysis is used to model the relationship between two or more variables in order to determine the strength and direction of the relationship. There are several types of regression analysis, including linear regression, logistic regression, and multiple regression.

Factor Analysis

Factor analysis is used to identify underlying factors or dimensions in a set of variables. This can be used to reduce the complexity of the data and identify patterns in the data.

Structural Equation Modeling (SEM)

SEM is a statistical technique used to model complex relationships between variables. It can be used to test complex theories and models of causality.

Cluster Analysis

Cluster analysis is used to group similar cases or observations together based on similarities or differences in their characteristics.

Time Series Analysis

Time series analysis is used to analyze data collected over time in order to identify trends, patterns, or changes in the data.

Multilevel Modeling

Multilevel modeling is used to analyze data that is nested within multiple levels, such as students nested within schools or employees nested within companies.

Applications of Experimental Design 

Experimental design is a versatile research methodology that can be applied in many fields. Here are some applications of experimental design:

• Medical Research: Experimental design is commonly used to test new treatments or medications for various medical conditions. This includes clinical trials to evaluate the safety and effectiveness of new drugs or medical devices.
• Agriculture : Experimental design is used to test new crop varieties, fertilizers, and other agricultural practices. This includes randomized field trials to evaluate the effects of different treatments on crop yield, quality, and pest resistance.
• Environmental science: Experimental design is used to study the effects of environmental factors, such as pollution or climate change, on ecosystems and wildlife. This includes controlled experiments to study the effects of pollutants on plant growth or animal behavior.
• Psychology : Experimental design is used to study human behavior and cognitive processes. This includes experiments to test the effects of different interventions, such as therapy or medication, on mental health outcomes.
• Engineering : Experimental design is used to test new materials, designs, and manufacturing processes in engineering applications. This includes laboratory experiments to test the strength and durability of new materials, or field experiments to test the performance of new technologies.
• Education : Experimental design is used to evaluate the effectiveness of teaching methods, educational interventions, and programs. This includes randomized controlled trials to compare different teaching methods or evaluate the impact of educational programs on student outcomes.
• Marketing : Experimental design is used to test the effectiveness of marketing campaigns, pricing strategies, and product designs. This includes experiments to test the impact of different marketing messages or pricing schemes on consumer behavior.

Examples of Experimental Design 

Here are some examples of experimental design in different fields:

• Example in Medical research : A study that investigates the effectiveness of a new drug treatment for a particular condition. Patients are randomly assigned to either a treatment group or a control group, with the treatment group receiving the new drug and the control group receiving a placebo. The outcomes, such as improvement in symptoms or side effects, are measured and compared between the two groups.
• Example in Education research: A study that examines the impact of a new teaching method on student learning outcomes. Students are randomly assigned to either a group that receives the new teaching method or a group that receives the traditional teaching method. Student achievement is measured before and after the intervention, and the results are compared between the two groups.
• Example in Environmental science: A study that tests the effectiveness of a new method for reducing pollution in a river. Two sections of the river are selected, with one section treated with the new method and the other section left untreated. The water quality is measured before and after the intervention, and the results are compared between the two sections.
• Example in Marketing research: A study that investigates the impact of a new advertising campaign on consumer behavior. Participants are randomly assigned to either a group that is exposed to the new campaign or a group that is not. Their behavior, such as purchasing or product awareness, is measured and compared between the two groups.
• Example in Social psychology: A study that examines the effect of a new social intervention on reducing prejudice towards a marginalized group. Participants are randomly assigned to either a group that receives the intervention or a control group that does not. Their attitudes and behavior towards the marginalized group are measured before and after the intervention, and the results are compared between the two groups.

When to use Experimental Research Design 

Experimental research design should be used when a researcher wants to establish a cause-and-effect relationship between variables. It is particularly useful when studying the impact of an intervention or treatment on a particular outcome.

Here are some situations where experimental research design may be appropriate:

• When studying the effects of a new drug or medical treatment: Experimental research design is commonly used in medical research to test the effectiveness and safety of new drugs or medical treatments. By randomly assigning patients to treatment and control groups, researchers can determine whether the treatment is effective in improving health outcomes.
• When evaluating the effectiveness of an educational intervention: An experimental research design can be used to evaluate the impact of a new teaching method or educational program on student learning outcomes. By randomly assigning students to treatment and control groups, researchers can determine whether the intervention is effective in improving academic performance.
• When testing the effectiveness of a marketing campaign: An experimental research design can be used to test the effectiveness of different marketing messages or strategies. By randomly assigning participants to treatment and control groups, researchers can determine whether the marketing campaign is effective in changing consumer behavior.
• When studying the effects of an environmental intervention: Experimental research design can be used to study the impact of environmental interventions, such as pollution reduction programs or conservation efforts. By randomly assigning locations or areas to treatment and control groups, researchers can determine whether the intervention is effective in improving environmental outcomes.
• When testing the effects of a new technology: An experimental research design can be used to test the effectiveness and safety of new technologies or engineering designs. By randomly assigning participants or locations to treatment and control groups, researchers can determine whether the new technology is effective in achieving its intended purpose.

How to Conduct Experimental Research

Here are the steps to conduct Experimental Research:

• Identify a Research Question : Start by identifying a research question that you want to answer through the experiment. The question should be clear, specific, and testable.
• Develop a Hypothesis: Based on your research question, develop a hypothesis that predicts the relationship between the independent and dependent variables. The hypothesis should be clear and testable.
• Design the Experiment : Determine the type of experimental design you will use, such as a between-subjects design or a within-subjects design. Also, decide on the experimental conditions, such as the number of independent variables, the levels of the independent variable, and the dependent variable to be measured.
• Select Participants: Select the participants who will take part in the experiment. They should be representative of the population you are interested in studying.
• Randomly Assign Participants to Groups: If you are using a between-subjects design, randomly assign participants to groups to control for individual differences.
• Conduct the Experiment : Conduct the experiment by manipulating the independent variable(s) and measuring the dependent variable(s) across the different conditions.
• Analyze the Data: Analyze the data using appropriate statistical methods to determine if there is a significant effect of the independent variable(s) on the dependent variable(s).
• Draw Conclusions: Based on the data analysis, draw conclusions about the relationship between the independent and dependent variables. If the results support the hypothesis, then it is accepted. If the results do not support the hypothesis, then it is rejected.
• Communicate the Results: Finally, communicate the results of the experiment through a research report or presentation. Include the purpose of the study, the methods used, the results obtained, and the conclusions drawn.

Purpose of Experimental Design 

The purpose of experimental design is to control and manipulate one or more independent variables to determine their effect on a dependent variable. Experimental design allows researchers to systematically investigate causal relationships between variables, and to establish cause-and-effect relationships between the independent and dependent variables. Through experimental design, researchers can test hypotheses and make inferences about the population from which the sample was drawn.

Experimental design provides a structured approach to designing and conducting experiments, ensuring that the results are reliable and valid. By carefully controlling for extraneous variables that may affect the outcome of the study, experimental design allows researchers to isolate the effect of the independent variable(s) on the dependent variable(s), and to minimize the influence of other factors that may confound the results.

Experimental design also allows researchers to generalize their findings to the larger population from which the sample was drawn. By randomly selecting participants and using statistical techniques to analyze the data, researchers can make inferences about the larger population with a high degree of confidence.

Overall, the purpose of experimental design is to provide a rigorous, systematic, and scientific method for testing hypotheses and establishing cause-and-effect relationships between variables. Experimental design is a powerful tool for advancing scientific knowledge and informing evidence-based practice in various fields, including psychology, biology, medicine, engineering, and social sciences.

Advantages of Experimental Design 

Experimental design offers several advantages in research. Here are some of the main advantages:

• Control over extraneous variables: Experimental design allows researchers to control for extraneous variables that may affect the outcome of the study. By manipulating the independent variable and holding all other variables constant, researchers can isolate the effect of the independent variable on the dependent variable.
• Establishing causality: Experimental design allows researchers to establish causality by manipulating the independent variable and observing its effect on the dependent variable. This allows researchers to determine whether changes in the independent variable cause changes in the dependent variable.
• Replication : Experimental design allows researchers to replicate their experiments to ensure that the findings are consistent and reliable. Replication is important for establishing the validity and generalizability of the findings.
• Random assignment: Experimental design often involves randomly assigning participants to conditions. This helps to ensure that individual differences between participants are evenly distributed across conditions, which increases the internal validity of the study.
• Precision : Experimental design allows researchers to measure variables with precision, which can increase the accuracy and reliability of the data.
• Generalizability : If the study is well-designed, experimental design can increase the generalizability of the findings. By controlling for extraneous variables and using random assignment, researchers can increase the likelihood that the findings will apply to other populations and contexts.

Limitations of Experimental Design

Experimental design has some limitations that researchers should be aware of. Here are some of the main limitations:

• Artificiality : Experimental design often involves creating artificial situations that may not reflect real-world situations. This can limit the external validity of the findings, or the extent to which the findings can be generalized to real-world settings.
• Ethical concerns: Some experimental designs may raise ethical concerns, particularly if they involve manipulating variables that could cause harm to participants or if they involve deception.
• Participant bias : Participants in experimental studies may modify their behavior in response to the experiment, which can lead to participant bias.
• Limited generalizability: The conditions of the experiment may not reflect the complexities of real-world situations. As a result, the findings may not be applicable to all populations and contexts.
• Cost and time : Experimental design can be expensive and time-consuming, particularly if the experiment requires specialized equipment or if the sample size is large.
• Researcher bias : Researchers may unintentionally bias the results of the experiment if they have expectations or preferences for certain outcomes.
• Lack of feasibility : Experimental design may not be feasible in some cases, particularly if the research question involves variables that cannot be manipulated or controlled.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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14.2: Design of experiments via factorial designs

• Last updated
• Save as PDF
• Page ID 22537

• Jocelyn Anleitner, Stephanie Combs, Diane Feldkamp, Heeral Sheth, Jason Bourgeois, Michael Kravchenko, Nicholas Parsons, & Andrew Wang
• University of Michigan

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Factorial design is an important method to determine the effects of multiple variables on a response. Traditionally, experiments are designed to determine the effect of ONE variable upon ONE response. R.A. Fisher showed that there are advantages by combining the study of multiple variables in the same factorial experiment. Factorial design can reduce the number of experiments one has to perform by studying multiple factors simultaneously. Additionally, it can be used to find both main effects (from each independent factor) and interaction effects (when both factors must be used to explain the outcome). However, factorial design can only give relative values, and to achieve actual numerical values the math becomes difficult, as regressions (which require minimizing a sum of values) need to be performed. Regardless, factorial design is a useful method to design experiments in both laboratory and industrial settings.

Factorial design tests all possible conditions. Because factorial design can lead to a large number of trials, which can become expensive and time-consuming, factorial design is best used for a small number of variables with few states (1 to 3). Factorial design works well when interactions between variables are strong and important and where every variable contributes significantly.

What is Factorial Design?

Factorial design example.

The easiest way to understand how factorial design works is to read an example. Suppose that you, a scientist working for the FDA, would like to study and measure the probability of patients suffering from seizures after taking a new pharmaceutical drug called CureAll. CureAll is a novel drug on the market and can cure nearly any ailment of the body. You along with your co-workers at the FDA have decided to test two dosage levels: 5 mg and 10 mg. You are also interested in determining whether the drug side-effects differ between younger adults (age 20) and older adults (age 40). Based on the given information, you see that there are two factors: dosage and age. Factors are the main categories to explore when determining the cause of seizures in patients. Under each of these factors, there are different levels: 5 and 10 mg for the dosage; 20 and 40 years for age. A level is basically one of the subdivisions that make up a factor. From this information, we can see that we have a 2 x 2 factorial design, which means that we will have 2 * 2 = 4 groups. A group is set of conditions that will make up that particular experiment.

Null Outcome

A null outcome situation is when the outcome of your experiment is the same regardless of how the levels within your experiment were combined. From the example above, a null outcome would exist if you received the same percentage of seizures occurring in patients with varying dose and age. The graphs below illustrate no change in the percentage of seizures for all factors, so you can conclude that the chance of suffering from a seizure is not affected by the dosage of the drug or the age of the patient.

Main Effects

A main effects situation is when there exists a consistent trend among the different levels of a factor. From the example above, suppose you find that as dosage increases, the percentage of people who suffer from seizures increases as well. You also notice that age does not play a role; both 20 and 40 year olds suffer the same percentage of seizures for a given amount of CureAll. From this information, you can conclude that the chance of a patient suffering a seizure is minimized at lower dosages of the drug (5 mg). The second graph illustrates that with increased drug dosage there is an increased percentage of seizures, while the first graph illustrates that with increased age there is no change in the percentage of seizures. Both of these graphs only contain one main effect, since only dose has an effect the percentage of seizures. Whereas, graphs three and four have two main effects, since dose and age both have an effect on the percentage of seizures.

Interaction Effects

The interaction effects situation is the last outcome that can be detected using factorial design. From the example above, suppose you find that 20 year olds will suffer from seizures 10% of the time when given a 5 mg CureAll pill, while 20 year olds will suffer 25% of the time when given a 10 mg CureAll pill. When 40 year olds, however, are given a 5 mg pill or a 10 mg pill, 15% suffer from seizures at both of these dosages. This correlation can be seen in the graphs below. There is an increasing chance of suffering from a seizure at higher doses for 20 year olds, but no difference in suffering from seizures for 40 year olds. Thus, there must be an interaction effect between the dosage of CureAll, and the age of the patient taking the drug. When you have an interaction effect it is impossible to describe your results accurately without mentioning both factors. You can always spot an interaction in the graphs because when there are lines that are not parallel an interaction is present. If you observe the main effect graphs above, you will notice that all of the lines within a graph are parallel. In contrast, for interaction effect graphs, you will see that the lines are not parallel.

Mathematical Analysis Approach

In the previous section, we looked at a qualitative approach to determining the effects of different factors using factorial design. Now we are going to shift gears and look at factorial design in a quantitative approach in order to determine how much influence the factors in an experiment have on the outcome.

How to Deal with a 2 n Factorial Design

Suppose you have two variables \(A\) and \(B\) and each have two levels a 1 , a 2 and b 1 , b 2 . You would measure combination effects of \(A\) and \(B\) (a 1 b 1 , a 1 b 2 , a 2 b 1 , a 2 b 2 ). Since we have two factors, each of which has two levels, we say that we have a 2 x 2 or a 2 2 factorial design. Typically, when performing factorial design, there will be two levels, and n different factors. Thus, the general form of factorial design is 2 n .

In order to find the main effect of \(A\), we use the following equation:

\[A = (a_2b_1 - a_1b_1) + (a_2b_2 - a_1b_2) \nonumber \]

Similarly, the main effect of B is given by:

\[B = (b_2a_1 - b_1a_1) + (b_2a_2 - b_1a_2) \nonumber \]

By the traditional experimentation, each experiment would have to be isolated separately to fully find the effect on B. This would have resulted in 8 different experiments being performed. Note that only four experiments were required in factorial designs to solve for the eight values in A and B. This shows how factorial design is a timesaver.

By taking the coefficients in A and B, the table below was created.

AB is found by multiplying the coefficients of a x b x to get the new coefficient effect.

The additional complication is the fact that more than one trial/replication is required for accuracy, so this requires adding up each sub-effect (e.g adding up the three trials of a 1 b 1 ). By adding up the coefficient effects with the sub-effects (multiply coefficient with sub-effect), a total factorial effect can be found. This value will determine if the factor has a significant effect on the outcome. For larger numbers, the factor can be considered extremely important and for smaller numbers, the factor can be considered less important. The sign of the number also has a direct correlation to the effect being positive or negative.

To get a mean factorial effect, the totals needs to be divided by 2 times the number of replicates , where a replicate is a repeated experiment.

\[\text {mean factorial effect} = \dfrac{\text{total factorial effect}}{2r} \nonumber \]

By adding a third variable (\(C\)), the process of obtaining the coefficients becomes significantly complicated. The main factorial effect for \(A\):

\[A=\left(a_{2} b_{1} c_{1}-a_{1} b_{1} c_{1}\right)+\left(a_{2} b_{2} c_{1}-a_{1} b_{2} c_{1}\right)+\left(a_{2} b_{1} c_{2}-a_{1} b_{1} c_{2}\right)+\left(a_{2} b_{2} c_{2}-a_{1} b_{2} c_{2}\right) \nonumber \]

The table of coefficients is listed below

It is clear that in order to find the total factorial effects, you would have to find the main effects of the variable and then the coefficients. Yates Algorithm can be used to simplify the process.

Yates Algorithm

Frank Yates created an algorithm to easily find the total factorial effects in a 2 n factorial that is easily programmable in Excel. While this algorithm is fairly straightforward, it is also quite tedious and is limited to 2 n factorial designs. Thus, modern technology has allowed for this analysis to be done using statistical software programs through regression.

• In the first column, list all the individual experimental combinations

According to the yates order, such as follows for a 2 3 factorial design

• In the second column, list all the totals for each combination
• The 1 st four entries in the third column (Stage 1) are obtained by adding pairs together from the "totals list" (previous column). The next four numbers are obtained by subtracting the top number from the bottom number of each pair.

• The fourth column (Stage 2) is obtained in the same fashion, but this time adding and subtracting pairs from Stage 1.

• The fifth column (Stage 3) is obtained in the same fashion, but this time adding and subtracting pairs from Stage 2.

• Continue with Stages until reaching n , or the number of factors. This final column is the Effect Total. A positive value means a positive correlation, and a negative values means a negative correlation. These values are all relative, however, so there is no way to compare different effect totals from different experiments.

Ignoring the first row, look in the last stage and find the variable that has the largest relative number, then that row indicates the MAIN TOTAL EFFECT . The Main Total Effect can be related to input variables by moving along the row and looking at the first column. If the row in the first column is a 2 b 1 c 1 then the main total effect is A. The row for a 1 b 2 c 1 would be for B. The row for a 2 b 1 c 2 would be for AC.

This main total effect value for each variable or variable combination will be some value that signifies the relationship between the output and the variable. For instance, if your value is positive, then there is a positive relationship between the variable and the output (i.e. as you increase the variable, the output increases as well). A negative value would signify a negative relationship. Notice, however, that the values are all relative to one another. So while the largest main total effect value in one set of experiments may have a value of 128, another experiment may have its largest main total effect value be 43. There is no way to determine if a value of 128 in one experiment has more control over its output than a value of 43 does, but for the purposes of comparing variables within an experiment, the main total effect does allow you to see the relative control the variables have on the output.

Factorial Design Example Revisited

Recall the example given in the previous section What is Factorial Design? In the example, there were two factors and two levels, which gave a 2 2 factorial design. The Yates Algorithm can be used in order to quantitatively determine which factor affects the percentage of seizures the most. For the use of the Yates algorithm, we will call age factor A with a 1 = 20 years, and a 2 = 40 years. Likewise, we will call dosage factor B, with b 1 = 5 mg, and b 2 = 10 mg. The data for the three outcomes is taken from the figures given in the example, assuming that the data given resulted from multiple trials.

The following Yates algorithm table using the data for the null outcome was constructed. As seen in the table, the values of the main total factorial effect are 0 for A, B, and AB. This proves that neither dosage or age have any effect on percentage of seizures.

Main Effect

The following Yates algorithm table using the data from the first two graphs of the main effects section was constructed. Besides the first row in the table, the row with the largest main total factorial effect is the B row, while the main total effect for A is 0. This means that dosage (factor B) affects the percentage of seizures, while age (factor A) has no effect, which is also what was seen graphically.

The following Yates algorithm table using the data from second two graphs of the main effects section was constructed. Besides the first row in the table, the main total effect value was 10 for factor A and 20 for factor B. This means that both age and dosage affect percentage seizures. However, since the value for B is larger, dosage has a larger effect on percentage of seizures than age. This is what was seen graphically, since the graph with dosage on the horizontal axis has a slope with larger magnitude than the graph with age on the horizontal axis.

Interaction Effect

The following Yates algorithm table was constructed using the data from the interaction effects section. Since the main total factorial effect for AB is non-zero, there are interaction effects. This means that it is impossible to correlate the results with either one factor or another; both factors must be taken into account.

Chemical Engineering Applications

It should be quite clear that factorial design can be easily integrated into a chemical engineering application. Many chemical engineers face problems at their jobs when dealing with how to determine the effects of various factors on their outputs. For example, suppose that you have a reactor and want to study the effect of temperature, concentration and pressure on multiple outputs. In order to minimize the number of experiments that you would have to perform, you can utilize factorial design. This will allow you to determine the effects of temperature and pressure while saving money on performing unnecessary experiments.

A 2007 study on converting wheat straw to fuel utilized factorial design to study the effect of four factors on the composition and susceptibility to enzyme hydrolysis of the final product. (Perez, et.al.). The table below shows the full factorial design for the study. The four factors that were studied all had only two levels and dealt with pretreatment parameters. They were: Water temperature, residence time, solid fraction and overpressure in the reactor. It is not necessary to understand what each of these are to understand the experimental design. As seen in the table below, there were sixteen trials, or 2^4 experiments.

Source: Perez, et. al.

Minitab DOE Example

Minitab 15 Statistical Software is a powerful statistics program capable of performing regressions, ANOVA, control charts, DOE, and much more. Minitab is especially useful for creating and analyzing the results for DOE studies. It is possible to create factorial, response surface, mixture, and taguchi method DOEs in Minitab. The general method for creating factorial DOEs is discussed below.

Creating Factorial DOE

Minitab provides a simple and user-friendly method to design a table of experiments. Additionally, analysis of multiple responses (results obtained from experimentation) to determine which parameters significantly affect the responses is easy to do with Minitab. Minitab 15 Statistical Software can be used via Virtual CAEN Labs by going to Start>All Programs>Math and Numerical Methods>Minitab Solutions>Minitab 15 Statistical Software.

The first step is creating the DOE by specifying the number of levels (typically 2) and number of responses. To do this, go to Stat>DOE>Factorial>Create Factorial Design as shown in the image below.

The next image is the "Create Factorial Design" options menu.

For a 2 level design, click the "2-level factorial (default generators)" radio button. Then specify the number of factors between 2 and 15. Other designs such as Plackett-Burman or a General full factorial design can be chosen. For information about these designs, please refer to the "Help" menu.

After the number of factors is chosen, click on the "Designs..." option to see the following menu.

In this menu, a 1/2 fraction or full factorial design can be chosen. Although the full factorial provides better resolution and is a more complete analysis, the 1/2 fraction requires half the number of runs as the full factorial design. In lack of time or to get a general idea of the relationships, the 1/2 fraction design is a good choice. Additionally, the number of center points per block, number of replicates for corner points, and number of blocks can be chosen in this menu. Consult the "Help" menu for details about these options. Click "Ok" once the type of design has been chosen.

Once the design has been chosen, the "Factors...", "Options..." and "Results..." buttons become active in the "Create Factorial Designs" option menu. Click on "Factors..." button to see the following menu.

The above image is for a 4 factor design. Factors A - D can be renamed to represent the actual factors of the system. The factors can be numeric or text. Additionally, a low and high value are initially listed as -1 and 1, where -1 is the low and 1 is the high value. The low and high levels for each factor can be changed to their actual values in this menu. Click "OK" once this is completed.

The necessary steps for creating the DOE are complete, but other options for "Results..." and "Options..." can be specified. The menus for "Results..." and "Options..." are shown below.

In the main "Create Factorial Design" menu, click "OK" once all specifications are complete. The following table is obtained for a 2-level, 4 factor, full factorial design. None of the levels were specified as they appear as -1 and 1 for low and high levels, respectively.

The above table contains all the conditions required for a full factorial DOE. Minitab displays the standard order and randomized run order in columns C1 and C2, respectively. Columns A-D are the factors. The first run (as specified by the random run order) should be performed at the low levels of A and C and the high levels of B and D. A total of 16 runs are required to complete the DOE.

Modifying DOE Table

Once a table of trials for the DOE has been created, additional modifications can be made as needed. Some typical modifications include modifying the name of each factors, specifying the high and low level of each factor, and adding replicates to the design. To being modifications of a current design, go to Stat>DOE>Modify Design... as seen in the figure below.

The following menu is displayed for modifying the design.

In the "Modify Design" menu, users can modify factors, replicate design, randomize design, renumber design, fold design, and add axial points. Additionally, any changes made can be put into a new worksheet. To change the factors, click the "Modify factors" radio button and then "Specify" to see the following options menu.

The default factors are named "A", "B", "C", and "D" and have respective high and low levels of 1 and -1. The name of the factors can be changed by simply clicking in the box and typing a new name. Additionally, the low and high levels for each factor can be modified in this menu. Since the high and low levels for each factor may not be known when the design is first created, it is convenient to be able to define them later. Click "OK" after modifications are complete.

Another typical modification is adding replicates to a design. Replicates are repeats of each trial that help determine the reproducibility of the design, thus increasing the number of trials and accuracy of the DOE. To add replicates, click the "Replicate design" radio button in the "Modify Design" menu. The following menu will be displayed.

The only option in this menu is the number of replicates to add. The number ranges between 1 and 10. To have a total of 3 trials of each, the user should add 2 replicates in this menu. If 4 replicates are added, there will be a total of 5 trials of each. Typically, if the same experimentation will occur for 3 lab periods, 2 replicates will be added.

Additional modifications to the design include randomizing and renumbering the design. These are very straightforward modifications which affect the ordering of the trials. For information about the "Fold design" and "Add axial points", consult the "Help" menu.

Analyzing DOE Results

After the complete DOE study has been performed, Minitab can be used to analyze the effect of experimental results (referred to as responses) on the factors specified in the design. The first step in analyzing the results is entering the responses into the DOE table. This is done much like adding data into an Excel data sheet. In the columns to the right of the last factor, enter each response as seen in the figure below.

The above figure contains three response columns. The names of each response can be changed by clicking on the column name and entering the desired name. In the figure, the area selected in black is where the responses will be inputted. For instance, if the purity, yield, and residual amount of catalyst was measured in the DOE study, the values of these for each trial would be entered in the columns.

Once the responses are entered, statistical analysis on the data can be performed. Go to Stat>DOE>Factorial>Analyze Factorial Design... as seen in the following image.

The menu that appears for analyzing factorial design is shown below.

In the "Analyze Factorial Design" menu, the responses are shown on the left of the screen. The first step is to choose the responses to be analyzed. All of the responses can be chosen at once or individually. To choose them, click (or click and drag to select many) and then click "Select" to add them into the "Responses:" section as seen below.

The next step is selecting which terms will be analyzed for the responses. To do this, click on "Terms..." and the following menu will appear.

The types of interactions between factors are chosen in this menu. For a first order model which excludes all factor-to-factor interactions, "1" should be chosen from the drop-down menu for "Include terms in the model up through order:". To include higher order terms and account for factor interactions, choose 2, 3, or 4 from the drop-down menu. Unless significant factor-to-factor interactions are expected, it is recommended to use a first order model which is a linear approximation.

Once the terms have been chosen, the next step is determining which graphs should be created. The types of graphs can be selected by clicking on "Graphs..." in the main "Analyze Factorial Design" menu.

In the Graphs menu shown above, the three effects plots for "Normal", "Half Normal", and "Pareto" were selected. These plots are different ways to present the statistical results of the analysis. Examples of these plots can be found in the Minitab Example for Centrifugal Contactor Analysis. The alpha value, which determines the limit of statistical significance, can be chosen in this menu also. Typically, the alpha value is 0.05. The last type of plots that can be chosen is residual plots. A common one to select is "Residuals versus fits" which shows how the variance between the predicted values from the model and the actual values.

The final option that must be specified is results. Click "Results..." from the "Analyze Factorial Design" menu to see the following screen.

In this menu, select all of the "Available Terms" and click the ">>" button to move them to the "Selected Terms". This will ensure that all the terms will be included in the analysis. Another feature that can be selected from this menu is to display the "Coefficients and ANOVA table" for the DOE study.

Other options can be selected from the "Analyze Factorial Design" menu such as "Covariates...", "Prediction...", "Storage...", and "Weights...". Consult the "Help" menu for descriptions of the other options. Once all desired changes have been made, click "OK" to perform the analysis. All of the plots will pop-up on the screen and a text file of the results will be generated in the session file.

Minitab Example for Centrifugal Contactor Analysis

Centrifugal Contactors, also known as Podbielniak (POD) centrifugal contactors, are used to purify a contaminated stream by counter-current, liquid-liquid extraction. Two immiscible fluids with different specific gravities are contacted counter-currently and the solute from the dirty stream is extracted by the clean stream. A common use for PODs methanol removal from biodiesel by contacting the stream with water. The amount of methanol remaining in the biodiesel (wt% MeOH) after the purification and the number of theoretical stages (No. Theor. Stages) obtained depend on the operating conditions of the POD. The four main operating parameters of the POD are rotational speed (RPM), ratio of biodiesel to water (Ratio), total flow rate of biodiesel and water (Flow Rate), and pressure (Pressure). A DOE study has been performed to determine the effect of the four operating conditions on the responses of wt% MeOH in biodiesel and number of theoretical stages achieved. (NOTE: The actual data for this example was made-up)

A 4-factor, 2-level DOE study was created using Minitab. Because experiments from the POD are time consuming, a half fraction design of 8 trial was used. The figure below contains the table of trials for the DOE.

After all the trials were performed, the wt% methanol remaining in the biodiesel and number of theoretical stages achieved were calculated. The figure below contains the DOE table of trials including the two responses.

Analysis was performed on the DOE study to determine the effects of each factor on the responses. Only first order terms were included in the analysis to create a linear model. Pareto charts for both wt% MeOH in biodiesel and number of theoretical stages are shown below.

The Pareto charts show which factors have statistically significant effects on the responses. As seen in the above plots, RPM has significant effects for both responses and pressure has a statistically significant effect on wt% methanol in biodiesel. Neither flow rate or ratio have statistically significant effects on either response. The Pareto charts are bar charts which allow users to easily see which factors have significant effects.

Half Normal Plots for wt% methanol in biodiesel and number of theoretical stages are shown below.

Like Pareto plots, Half Normal plots show which factors have significant effects on the responses. The factors that have significant effects are shown in red and the ones without significant effects are shown in black. The further a factor is from the blue line, the more significant effect it has on the corresponding response. For wt% methanol in biodiesel, RPM is further from the blue line than pressure, which indicates that RPM has a more significant effect on wt% methanol in biodiesel than pressure does.

The final plot created is the Normal Effect Plot. The Normal Plot is similar to the Half Normal plot in design. However, the Normal Plot displays whether the effect of the factor is positive or negative on the response. The Normal Plots for the responses are shown below.

As seen above, RPM is shown with a positive effect for number of theoretical stages, but a negative effect for wt% methanol in biodiesel. A positive effect means that as RPM increases, the number of theoretical stages increases. Whereas a negative effect indicates that as RPM increases, the wt% methanol in biodiesel decreases. Fortunately for operation with the POD, these are desired results. When choosing operating conditions for the POD, RPM should be maximized to minimize the residual methanol in biodiesel and maximize the number of theoretical stages achieved.

In addition to the above effects plots, Minitab calculates the coefficients and constants for response equations. The response equations can be used as models for predicting responses at different operating conditions (factors). The coefficients and constants for wt% methanol in biodiesel and number of theoretical stages are shown below.

Since this is a first order, linear model, the coefficients can be combined with the operating parameters to determine equations. The equations from this model are shown below.

These equations can be used as a predictive model to determine wt% methanol in biodiesel and number of theoretical stages achieved at different operating conditions without actually performing the experiments. However, the limits of the model should be tested before the model is used to predict responses at many different operating conditions.

Example \(\PageIndex{1}\)

You have been employed by SuperGym, a local personal training gym, who want an engineer's perspective on how to offer the best plans to their clients. SuperGym currently categorizes her clients into 4 body types to help plan for the best possible program.

• Type 1 - Very healthy
• Type 2 - Needs tone
• Type 3 - Needs strength
• Type 4 - Needs tone and strength

In addition, SuperGym offers 4 different workout plans, A through D, none of which are directly catered to any of the different types. Create an experimental factorial design that could be used to test the effects of the different workout plans on the different types of people at the gym.

In order to solve this problem, we need to determine how many different experiments would need to be performed. In order to solve this, we can see that we have two different factors, body type and workout plan. For each factor, there exist four different levels. Thus, we have a 4 2 factorial design, which gives us 16 different experimental groups. Creating a table of all of the different groups, we arrive at the following factorial design:

Where A-D is the workout plan and 1-4 is the types

Example \(\PageIndex{2}\)

Suppose that you are looking to study the effects of hours slept (A), hours spent with significant other (B), and hours spent studying (C) on a students exam scores. You are given the following table that relates the combination of these factors and the students scores over the course of a semester. Use the Yates method in order to determine the effect each variable on the students performance in the course.

Using the approach introduced earlier in this article, we arrive at the following Yates solution.

From this table, we can see that there is positive correlation for factors A and C, meaning that more sleep and more studying leads to a better test grade in the class. Factor B, however, has a negative effect, which means that spending time with your significant other leads to a worse test score. The lesson here, therefore, is to spend more time sleeping and studying, and less time with your boyfriend or girlfriend.

Example \(\PageIndex{3}\)

Your mom is growing a garden for the state fair and has done some experiments to find the ideal growing condition for her vegetables. She asks you for help interpreting the results and shows you the following data:

Make plots to determine the main or interaction effects of each factor.

Here is the plot you should have gotten for the given data.

From this one can see that there is an interaction effect since the lines cross. One cannot discuss the results without speaking about both the type of fertilizer and the amount of water used. Using fertilizer A and 500 mL of water resulted in the largest plant, while fertilizer A and 350 mL gave the smallest plant. Fertilizer B and 350 mL gave the second largest plant, and fertilizer B and 500 mL gave the second smallest plant. There is clearly an interaction due to the amount of water used and the fertilizer present. Perhaps each fertilizer is most effective with a certain amount of water. In any case, your mom has to consider both the fertilizer type and amount of water provided to the plants when determining the proper growing conditions.

Exercise \(\PageIndex{1}\)

Which of the following is not an advantage of the use of factorial design over one factor design?

• More time efficient
• Provides how each factor effects the response
• Does not require explicit testing
• Does not require regression

Exercise \(\PageIndex{2}\)

In a 2 2 factorial design experiment, a total main effect value of -5 is obtained. This means that

• there is a relative positive correlation between the two factors
• there is no correlation between the two factors
• there is a relative negative correlation between the two factors
• there is either a positive or negative relative correlation between the two factors
• Box, George E.P., et. al. "Statistics for Engineers: An Introduction to Design, Data Analysis, and Model Building." New York: John Wiley & Sons.
• Trochim, William M.K. 2006. "Factorial Designs." Research Methods Knowledge Base. < http://www.socialresearchmethods.net/kb/expfact.htm >
• Perez, Jose A., et. al. "Effect of process variables on liquid hot water pretreatment of wheat straw for bioconversion to fuel-ethanol in a batch reactor." Journal of Chemical Technology & Biotechnology. Volume 82, Issue 10, Pages 929-938. Published Online Sep 3, 2007.

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• Published: 15 May 2024

Arresting failure propagation in buildings through collapse isolation

• Nirvan Makoond   ORCID: orcid.org/0000-0002-5203-6318 1 ,
• Andri Setiawan   ORCID: orcid.org/0000-0003-2791-6118 1 ,
• Manuel Buitrago   ORCID: orcid.org/0000-0002-5561-5104 1 &
• Jose M. Adam   ORCID: orcid.org/0000-0002-9205-8458 1  

Nature volume  629 ,  pages 592–596 ( 2024 ) Cite this article

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• Civil engineering
• Mechanical engineering

Several catastrophic building collapses 1 , 2 , 3 , 4 , 5 occur because of the propagation of local-initial failures 6 , 7 . Current design methods attempt to completely prevent collapse after initial failures by improving connectivity between building components. These measures ensure that the loads supported by the failed components are redistributed to the rest of the structural system 8 , 9 . However, increased connectivity can contribute to collapsing elements pulling down parts of a building that would otherwise be unaffected 10 . This risk is particularly important when large initial failures occur, as tends to be the case in the most disastrous collapses 6 . Here we present an original design approach to arrest collapse propagation after major initial failures. When a collapse initiates, the approach ensures that specific elements fail before the failure of the most critical components for global stability. The structural system thus separates into different parts and isolates collapse when its propagation would otherwise be inevitable. The effectiveness of the approach is proved through unique experimental tests on a purposely built full-scale building. We also demonstrate that large initial failures would lead to total collapse of the test building if increased connectivity was implemented as recommended by present guidelines. Our proposed approach enables incorporating a last line of defence for more resilient buildings.

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Disasters recorded from 2000 to 2019 are estimated to have caused economic losses of US$2.97 trillion and claimed approximately 1.23 million lives 11 . Most of these losses can be attributed to building collapses 12 , which are often characterized by the propagation of local-initial failures 13 that can arise because of extreme or abnormal events such as earthquakes 13 , 14 , 15 , 16 , floods 17 , 18 , 19 , 20 , storms 21 , 22 , landslides 23 , 24 , explosions 25 , vehicle impacts 26 and even construction or design errors 6 , 26 . As the world faces increasing trends in the frequency and intensity of extreme events 27 , 28 , it is arguably now more important than ever to design robust structures that are insensitive to initial damage 13 , 29 , irrespective of the underlying threat causing it.

Most robustness design approaches used at present 8 , 9 , 30 , 31 aim to completely prevent collapse initiation after a local failure by providing extensive connectivity within a structural system. Although these measures can ensure that the load supported by a failed component is redistributed to the rest of the structure, they are neither viable nor sustainable when considering larger initial failures 13 , 25 , 32 . In these situations, the implementation of these approaches can even result in collapsing parts of the building pulling down the rest of the structure 10 . The fact that several major collapses have occurred because of large initial failures 6 raises serious concerns about the inadequacy of the current robustness measures.

Traditionally, research in this area has focused on preventing collapse initiation after initial failures rather than on preventing collapse propagation. This trend dates back to the first impactful studies in the field of structural robustness, which were performed after a lack of connectivity enabled the progressive collapse of part of the Ronan Point tower in 1968 (ref.  33 ). Although completely preventing any collapse is certainly preferable to limiting the extent of a collapse, the occurrence of unforeseeable incidents is inevitable 34 and major building collapses keep occurring 1 , 2 , 3 .

Here we present an original approach for designing buildings to isolate the collapse triggered by a large initial failure. The approach, which is based on controlling the hierarchy of failures in a structural system, is inspired by how lizards shed their tails to escape predators 35 . The proposed hierarchy-based collapse isolation design ensures sufficient connectivity for operational conditions and after local-initial failures for which collapse initiation can be completely prevented through load redistribution. These local-initial failures can even be greater than those considered by building codes. Simultaneously, the structural system is also designed to separate into different parts and isolate a collapse when its propagation would otherwise be inevitable. As in the case of lizard tail autotomy 35 , this is achieved by promoting controlled fracture along predefined segment borders to limit failure propagation. In this work, hierarchy-based collapse isolation is applied to framed building structures. Developing this approach required a precise characterization of the collapse propagation mechanisms that need to be controlled. This was achieved using computational simulations that were validated through a specifically designed partial collapse test of a full-scale building. The obtained results demonstrate the viability of incorporating hierarchy-based collapse isolation in building design.

Hierarchy-based collapse isolation

Hierarchy-based collapse isolation design makes an important distinction between two types of initial failures. The first, referred to as small initial failures, includes all failures for which it is feasible to completely prevent the initiation of collapse by redistributing loads to the remaining structural system. The second type of initial failure, referred to as large initial failures, includes more severe failures that inevitably trigger at least a partial collapse.

The proposed design approach aims to (1) arrest unimpeded collapse propagation caused by large initial failures and (2) ensure the ability of a building to develop alternative load paths (ALPs) to prevent collapse initiation after small initial failures. This is achieved by prioritizing a specific hierarchy of failures among the components on the boundary of a moving collapse front.

Buildings are complex three-dimensional structural systems consisting of different components with very specific functions for transferring loads to the ground. Among these, vertical load-bearing components such as columns are the most important for ensuring global structural stability and integrity. Therefore, hierarchy-based collapse isolation design prevents the successive failure of columns, which would otherwise lead to catastrophic collapse. Although the exact magnitude of dynamic forces transmitted to columns during a collapse process is difficult to predict, these forces are eventually limited by the connections between columns and floor systems. In the proposed approach, partial-strength connections are designed to limit the magnitude of transmitted forces to values that are lower than the capacity of columns to resist unbalanced forces (see section ‘ Building design ’). This requirement guarantees a specific hierarchy of failures during collapse, whereby connection failures always occur before column failures. As a result, the collapse following a large initial failure is always restricted to components immediately adjacent to those directly involved in the initial failure. However, it is still necessary to ensure a lower bound on connection strengths to activate ALPs after small initial failures. Therefore, cost-effective implementation of hierarchy-based collapse isolation design requires finding an optimal balance between reducing the strength of connections and increasing the capacity of columns.

To test and verify the application of our proposed approach, we designed a real 15 m × 12 m precast reinforced concrete building with two 2.6-m-high floors. This basic geometry represents a building size that can be built and tested at full-scale while still being representative of current practices in the construction sector. The structural type was selected because of the increasing use of prefabricated construction for erecting high-occupancy buildings such as hospitals and malls because of several advantages in terms of quality, efficiency and sustainability 36 .

The collapse behaviour of possible design options (Extended Data Fig. 1 ) subjected to both small and large initial failures was investigated using high-fidelity collapse simulations (Fig. 1 ) based on the applied element method (AEM; see section ‘ Modelling strategy ’). The ability of these simulations to accurately represent collapse phenomena for the type of building being studied was later validated by comparing its predictions to the structural response observed during a purposely designed collapse test of a full-scale building (Extended Data Fig. 2 and Supplementary Video  7 ).

a , Partial-strength beam–column connection optimized for hierarchy-based collapse isolation. b , Partial collapse of a building designed for hierarchy-based collapse isolation (design H) after the loss of a corner column and two penultimate-edge columns. c , Total collapse of conventional building design (design C) after the same large initial failure scenario.

Following the preliminary design of a structure to resist loads suitable for office buildings, two building design options considering different robustness criteria were further investigated (see section ‘ Building design ’). The first option, design H (hierarchy-based), uses optimized partial-strength connections and enhanced columns (Fig. 1a ) to fulfil the requirements of hierarchy-based collapse isolation design. The second option, design C (conventional), is strictly based on code requirements and provides a benchmark comparison for evaluating the effectiveness of the proposed approach. It uses full-strength connections to improve robustness as recommended in current guidelines 37 and building codes 8 , 9 .

Simulations predicted that both design H and design C could develop stable ALPs that are able to completely prevent the initiation of collapse after small initial failure scenarios that are more severe than those considered in building codes 8 , 9 (Extended Data Fig. 3 ).

When subjected to a larger initial failure, simulations predict that design H can isolate the collapse to only the region directly affected by the initial failure (Fig. 1b ). By contrast, design C, with increased connectivity, causes collapsing elements to pull down the rest of the structure, leading to total collapse (Fig. 1c ). These two distinct outcomes demonstrate that the prevention of unimpeded collapse propagation can only be ensured when hierarchy-based collapse isolation is implemented (Extended Data Fig. 4 and Supplementary Video  1 ).

Testing a full-scale precast building

To confirm the expected performance improvement that can be achieved with the hierarchy-based collapse isolation design, a full-scale building specimen corresponding to design H was purposely built and subjected to two phases of testing as part of this work (Fig. 2a and Supplementary Information  Sections 1 and 2 ). The precast structure was constructed with continuous columns cast together with corbels (Supplementary Video  4 ). The columns were cast with prepared dowel bars and sleeves for placing continuous top beam reinforcement bars through columns (Fig. 2b,c ). The bars used for these two types of reinforcing element (Fig. 1a ) were specifically selected to produce partial-strength connections. These connections are strong enough for the development of ALPs after small initial failures but weak enough to enable hierarchy-based collapse isolation after large initial failures.

a , Full-scale precast concrete structure and columns removed in different testing phases. The label used for each column is shown. The location of beams connecting the different columns is indicated by the dotted lines above the second-floor level. The expected collapse area in the second phase of testing is indicated. b , Typical first-floor connection before placement of beams during construction. c , Typical second-floor connection after placement of precast beams during construction. Both b and c show columns with two straight precast beams on either side (C2, C3, C6, C7, C10 and C11). d , Device used for quasi-static removal of two columns in the first phase of testing. e , Three-hinged mechanism used for dynamic removal of corner column in the second phase of testing.

After investigating different column-removal scenarios from different regions of the test building (see section ‘ Experiment and monitoring design ’, Extended Data Fig. 5 and Supplementary Video  2 ), two phases of testing were defined to capture relevant collapse-related phenomena and validate the effectiveness of hierarchy-based collapse isolation. Separating the test into two phases allowed two different aspects to be analysed: (1) the prevention of collapse initiation after small initial failures and (2) the isolation of collapse after large initial failures.

Phase 1 involved the quasi-static removal of two penultimate-edge columns using specifically designed removable supports (Fig. 2d and Extended Data Fig. 6 ). This testing phase corresponds to a small initial failure scenario for which design H was able to develop ALPs to prevent collapse initiation. Phase 2 reproduced a large initial failure through the dynamic removal of the corner column found between the two previously removed columns using a three-hinged collapsible column (Fig. 2e ).

During both testing phases, a distributed load (11.8 kN m −2 ) corresponding to almost twice the magnitude specified in Eurocodes 38 for accidental design situations (6 kN m −2 ) was imposed on bays expected to collapse in phase 2 (Fig. 2a and Supplementary Video  5 ). Predictive simulations indicated that the failure mode and overall collapse would be almost identical when comparing this partial loading configuration with that in which the entire building is loaded (Supplementary Video  3 ). However, the partial loading configuration turns out to be more demanding for the part of the structure expected to remain upright as evidenced by the greater drifts it produces during collapse (see section ‘ Experiment and monitoring design ’ and Extended Data Fig. 7 ). The structural response during all phases of testing was extensively monitored with an array of different sensors (see section ‘ Experiment and monitoring design ’ and Supplementary Information Section 3 ) that provided the information used as a basis for the analyses presented in the following sections.

Preventing collapse initiation

Collapse initiation was completely prevented after the removal of two penultimate-edge columns in phase 1 of testing (Fig. 3a ), demonstrating that design H complies with the robustness requirements included in current building standards 8 , 9 , 39 . As this initial failure scenario is more severe than those considered by standardized design methods 8 , 9 , 30 , it represents an extreme case for which ALPs are still effective. As such, the outcome of phase 1 demonstrates that implementing hierarchy-based collapse isolation design does not impair the ability of this structure to prevent collapse initiation.

a , Test building during phase 1 of testing after removal of columns C8 and C11. The beam depth ( h ) used to compute the ratio plotted in b is shown and the location of the strain measurement plotted in c is indicated. b , Evolution of beam deflection expressed as a ratio of beam depth at the location of removed column C11. The chord rotation of the beams bridging over this removed column is also indicated using a secondary vertical axis. c , Strain increase in continuity reinforcement in the second-floor beam between C12 and C11.

Source Data

Analysis of the structural response during phase 1 (Supplementary Information Section 4 ) shows that collapse was prevented because of the redistribution of loads through the beams (Fig. 3b,c ), columns (Extended Data Fig. 8 ) and slabs (Supplementary Report 4 ) adjacent to the removed columns. The beams bridging over the removed columns sustained loads through flexural action, as evidenced by the magnitude of the vertical displacement recorded at the removal locations (Fig. 3b ). These values were far too small to allow the development of catenary forces, which only begin to appear when displacements exceed the depth of the beam 40 .

The flexural response of the structure after the loss of two penultimate-edge columns was only able to develop because of the specific reinforcement detailing introduced in the design. This was verified by the increase in tensile strains recorded in the continuous beam reinforcement close to the removed column (Fig. 3c ) and in ties placed between the precast hollow-core planks in the floor system close to column C7 (Supplementary Information Section 4 ). The latter also proves that the slabs contributed notably to load redistribution after column removal.

In general, the structure experienced only small movements and suffered very little permanent damage during phase 1 (Supplementary Information Section 4 ), despite the high imposed loads used for testing. The only reinforcement bars showing some signs of yielding were the continuous reinforcement bars of beams close to the removed columns (Fig. 3c ).

Arresting collapse propagation

Following the removal of two penultimate-edge columns in phase 1, the sudden removal of the C12 corner column in phase 2 triggered a collapse that was arrested along the border delineated by columns C3, C7, C6 and C10 (Fig. 4a–d and Supplementary Video  6 ). Thus, the viability of hierarchy-based collapse isolation design is confirmed.

a , Collapse sequence during phase 2 of testing. b , Partial collapse of full-scale test building (design H) after the removal of three columns. The segment border in which collapse propagation was arrested is indicated. The axes shown at column C9 correspond to those used in f to indicate the changing direction of the resultant drift measured at this location. c , Failure of beam–column connections at collapse border. d , Debonding of reinforcement in the floor at collapse border. e , Change in average axial strains measured in column C7. A negative change represents an increase in compressive strains. f , Magnitude of resultant drift measured at C9. g , Change in direction of resultant drift measured at C9. The initial drift after phase 1 of testing and the residual drift after the upright part of the building stabilized are also shown in the plot.

During the initial stages following the removal of C12, the collapsing bays next to this column pulled up the columns on the opposite corner of the building (columns C1, C3 and C6). During this process, column C7 behaves like a pivot point, experiencing a significant increase in compressive forces (Fig. 4e and Supplementary Information Section 5 ). This phenomenon was enabled by the connectivity between collapsing parts and the rest of the structure. If allowed to continue, this could have led to successive column failures and unimpeded collapse propagation. However, during the test, the rupture of continuous reinforcement bars (Fig. 4c ) occurred as the connections failed and halted the transmission of forces to columns. These connection failures occurred before any column failures, as intended by the hierarchy-based collapse isolation design of the structural system. Specifically, this type of connection failure occurred at the junctions with the two columns (C7 and C10) immediately adjacent to the failure origin (around C8, C11 and C12), effectively segmenting the structure along the border shown in Fig. 4b . Segmentation along this border was completed by the total separation of the floor system, which was enabled by the debonding of slab reinforcements at the segment border (Fig. 4d and Supplementary Video  8 ).

Observing the building drift measured at the top of column C9 (Fig. 4f ) enabled us to better understand the nature of forces acting on the building further away from the collapsing region. The initial motion shows the direction of pulling forces generated by the collapsing elements (Fig. 4g ). This drift peaks very shortly after the point in time when separation of the collapsing parts occurs (Fig. 4f ). After this peak, the upright part of the structure recoiled backwards and experienced an attenuated oscillatory motion before finding a new stable equilibrium (Fig. 4g ). The magnitude of the measured peak drift is comparable to the drift limits considered in seismic regions when designing against earthquakes with a 2,500-year return period 41 (Supplementary Information Section 5 ). This indicates that the upright part of the structure was subjected to strong dynamic horizontal forces as it was effectively tugged by the collapsing elements falling to the ground. The building would have failed because of these unbalanced forces had hierarchy-based collapse isolation design not been implemented.

The upright building segment suffered permanent damages as evidenced by the residual drift recorded at the top of column C9 (Fig. 4g ). This is further corroborated by the fact that several reinforcement bars in this part of the structure yielded, particularly in areas close to the segment border (Supplementary Report 5 ). Despite the observed level of damage, safe evacuation and rescue of people from this building segment would still be possible after an extreme event, saving lives that would have been lost had a more conventional robustness design (design C) been used instead.

Discussion and future outlook

Our results demonstrate that the extensive connectivity adopted in conventional robustness design can lead to catastrophic collapse after large initial failures. To address this risk, we have developed and tested a collapse isolation design approach based on controlling the hierarchy of failures occurring during the collapse. Specifically, it is ensured that connection failures occur before column failures, mitigating the risk of collapse propagation throughout the rest of the structural system. The proposed approach has been validated through the partial collapse test of a full-scale precast building, showing that propagating collapses can be arrested at low cost without impairing the ability of the structure to completely prevent collapse initiation after small initial failures.

The reported findings show a last line of defence against major building collapses due to extreme events. This paves the way for the proposed solution to be developed, tested and implemented in different building types with different building elements. This discovery opens opportunities for robustness design that will lead to a new generation of solutions for avoiding catastrophic building collapses.

Building design

Our hierarchy-based collapse isolation approach ensures buildings have sufficient connectivity for operational conditions and small initial failures, yet separate into different parts and isolate a collapse after large initial failures. We chose a precast construction as our main structural system for our case study. A notable particularity of precast systems compared with cast-in-place buildings is that the required construction details can be implemented more precisely. We designed and systematically investigated two precast building designs: designs H and C.

Design H is our building design in which the hierarchy-based collapse isolation approach is applied. Design H was achieved after several preliminary iterations by evaluating various connections and construction details commonly adopted in precast structures. The final design comprises precast columns with corbels connected to a floor system (partially precast beams and hollow-core slabs) through partial-strength beam–column connections (Extended Data Fig. 1 and Supplementary Information Section 1 ). This partial-strength connection was achieved by (1) connecting the bottom part of the beam (precast) to optimally designed dowel bars anchored to the column corbels and (2) passing continuous top beam bars through the columns. With this partial-strength connection, we have more direct control over the magnitude of forces being transferred from the floor system to the columns, which is a key aspect for achieving hierarchy-based collapse isolation. The hierarchy of failures was initially implemented through the beam–column connections (local level) and later verified at the system (global) level.

At the local level, three main components are designed according to the hierarchy-based concept: (1) top continuity bars of the beams; (2) dowel bars connecting beams to corbels; and (3) columns.

Top continuity bars of beams: To allow the structural system to redistribute the loads after small initial failures, top reinforcement bars in all beams were specifically designed to fulfil structural robustness requirements (Extended Data Fig. 3 ). Particularly, we adopted the prescriptive tying rules (referred to as Tie Forces) of UFC 4-023-03 (ref.  9 ) to perform the design of the ties. The required tie strength F i in both the longitudinal and transverse directions for the internal beams is expressed as

For the peripheral beams, the required tie strength F P is expressed as

where  w F  = floor load (in kN m −2 );  D  = dead load (in kN m −2 );  L  = live load (in kN m −2 );  L 1  = greater of the distances between the centres of the columns, frames or walls supporting any two adjacent floor spaces in the direction under consideration (in m);  L P  = 1.0 m; and  W C  = 1.2 times dead load of cladding (neglected in this design).

These required tie strengths are fulfilled with three bars (20 mm diameter) for the peripheral beams and three bars (25 mm diameter) for the internal beams. These required reinforcement dimensions were implemented through the top bars of the beam and installed continuously (lap-spliced, internally, and anchored with couplers at the ends) throughout the building (Extended Data Fig. 1 ).

Dowel bars connecting the beam and corbel of the column: The design of the dowel bars is one of the key aspects in achieving partial-strength connections that fail at a specific threshold to enable segmentation. These dowel bars would control the magnitude of the internal forces between the floor system and column while allowing for some degree of rotational movement. The dowels were designed to resist possible failure modes using expressions proposed in the fib guidelines 37 . Several possible failure modes were checked: splitting of concrete around the dowel bars, shear failure of the dowel bars and forming a plastic hinge in the dowel. The shear capacity of a dowel bar loaded in pure shear can be determined according to the Von Mises yield criterion:

where f yd is the design yield strength of the dowel bar and A s is the cross-sectional area of the dowel bar. In case of concrete splitting failure, the highly concentrated reaction transferred from the dowel bar shall be designed to be safely spread to the surrounding concrete. The strut and tie method is recommended to perform such a design 42 . If shear failure and splitting of concrete do not occur prematurely, the dowel bar will normally yield in bending, indicated by the formation of a plastic hinge. This failure mode is associated with a significant tensile strain at the plastic hinge location of the dowel bar and the crushing of concrete around the compression part of the dowel. The shear resistance achieved at this state for dowel (ribbed) bars across a joint of a certain width (that is, the neoprene bearing) can be expressed as

where α 0 is a coefficient that considers the bearing strength of concrete and can be taken as 1.0 for design purposes, α e is a coefficient that considers the eccentricity, e is the load eccentricity and shall be computed as the half of the joint width (half of the neoprene bearing thickness), Φ and A s are the diameter and the cross-sectional area of the dowel bar, respectively, f cd,max is the design concrete compressive strength at the stronger side, σ sn is the local axial stress of the dowel bar at the interface location, \({f}_{{\rm{yd}},{\rm{red}}}={f}_{{\rm{yd}}}-{\sigma }_{{\rm{sn}}}\) is the design yield strength available for dowel action, f yd is the yield strength of the dowel bar and μ is the coefficient of friction between the concrete and neoprene bearing. By performing the checks on these three possible failure modes, we selected the final (optimum) design with a two dowel bars (20 mm diameter) configuration.

Columns: The proposed hierarchy-based approach requires columns to have adequate capacity to resist the internal forces transmitted by the floor system during a collapse. By fulfilling this strength hierarchy, we can ensure and control that failure happens at the connections first before the columns fail, thus preventing collapse propagation. The columns were initially designed according to the general procedure prescribed by building standards. Then, the resulting capacity was verified using the modified compression field theory (MCFT) 43 to ensure that it was higher than the maximum expected forces transmitted by the connection to the floor system. MCFT was derived to consistently fulfil three main aspects: equilibrium of forces, compatibility and rational stress–strain relationships of cracked concrete expressed as average stresses and strains. The principal compressive stress in the concrete f c 2 is expressed not only as a function of the principal compressive strain ε 2 but also of the co-existing principal tensile strain ε 1 , known as the compression softening effect:

where f c 2max is the peak concrete compressive strength considering the perpendicular tensile strain, \({f}_{c}^{{\prime} }\) is the uniaxial compressive strength, and \({\varepsilon }_{{c}^{{\prime} }}\) is the peak uniaxial concrete compressive strain and can be taken as −0.002. In tension, concrete is assumed to behave linearly until the tensile strength is achieved, followed by a specific decaying function 43 . Regarding aggregate interlock, the shear stress that can be transmitted across cracks v ci is expressed as a function of the crack width w , and the required compressive stress on the crack f ci (ref.  44 ):

where a refers to the maximum aggregate size in mm and the stresses are expressed in MPa. The MCFT analytical model was implemented to solve the sectional and full-member response of beams and columns subjected to axial, bending and shear in Response 2000 software (open access) 45 , 46 . In Response 2000, we input key information, including the geometries of the columns, reinforcement configuration and the material definition for the concrete and the reinforcing bars. Based on this information, we computed the M – V (moment and shear interaction envelope) and M – N (moment and axial interaction envelope) diagrams that represent the capacity of the columns. The results shown in Extended Data Fig. 4 about the verification of the demand and capacity envelopes were obtained using the analytical procedure described here.

At the global level, the initially collapsing regions of the building generate a significant magnitude of dynamic unbalanced forces. The rest of the building system must collectively resist these unbalanced forces to achieve a new equilibrium state. Depending on the design of the structure, this phenomenon can lead to two possible scenarios: (1) major collapse due to failure propagation or (2) partial collapse only of the initially affected regions. The complex interaction between the three-dimensional structural system and its components must be accounted for to evaluate the structural response during collapse accurately. Advanced computational simulations, described in the ‘ Modelling strategy ’ section, were adopted to analyse the global building to verify that major collapse can be prevented. The final design obtained from the local-level analysis (top continuity bars, dowel bars and columns) was used as an input for performing the global computational simulations. Certain large initial failures deemed suitable for evaluating the performance of this building were simulated. In case failure propagation occurs, the original hierarchy-based design must be further adapted. An iterative process is typically required involving several simulations with various building designs to achieve an optimum result that balances the cost and desired collapse performance. The final iteration of design H, which fulfils both the local and global hierarchy checks, is provided in Extended Data Fig. 1 .

Design C is a conventional building design that complies with current robustness standards but does not explicitly fulfil our hierarchy-based approach. The same continuity bars used in design H were used in design C. We adopted a full-strength connection as recommended by the fib guideline 37 . The guideline promotes full connectivity to enhance the development of alternative load paths for preventing collapse initiation. In design C, we used a two dowel bars (32 mm diameter) configuration to ensure full connectivity when the beams are working at their maximum flexural capacity. Another main difference was that the columns in design C were designed according to codes and current practice (optimal solution) without explicitly checking that hierarchy-based collapse isolation criteria are fulfilled. The final design of the columns and connections adopted in design C is provided in Extended Data Fig. 1 .

Modelling strategy

We used the AEM implemented in the Extreme Loading for Structures software to perform all the computational simulations presented in this study 47 (Extended Data Figs. 2 – 5 and 7 and Supplementary Videos  1 , 2 , 3 and 7 ). We chose the AEM for its ability to represent all phases of a structural collapse efficiently and accurately, including element separation (fracture), contact and collision 47 . The method discretizes a continuum into small, finite-size elements (rigid bodies) connected using multiple normal and shear springs distributed across each element face. Each element has six degrees of freedom, three translational and three rotational, at its centre, whereas the behaviour of the springs represents all material constitutive models, contact and collision response. Despite the simplifying assumptions in its formulation 48 , its ability to accurately account for large displacements 49 , cyclic loading 50 , as well as the effects of element separation, contact and collision 51 has been demonstrated through many comparisons with experimental and theoretical results 47 .

Geometric and physical representations

We modelled each of the main structural components of the building separately, including the columns, beams, corbels and hollow-core slabs. We adopted a consistent mesh size with an average (representative) size of 150 mm. Adopting this mesh configuration resulted in a total number of 98,611 elements. We defined a specialized interface with no tensile or shear strength between the precast and cast-in-situ parts to allow for localized deformations that occur at these locations. The behaviour of the interface was mainly governed by a friction coefficient of 0.6, which was defined according to concrete design guidelines 52 , 53 , 54 . The normal stiffness of these interfaces corresponded to the stiffness of the concrete cast-in-situ topping. The elastomeric bearing pads supporting the precast beams on top of the corbels were also modelled with a similar interface having a coefficient of friction of 0.5 (ref.  55 ).

Element type and constitutive models

We adopted an eight-node hexahedron (cube) element with the so-called matrix-springs connecting adjacent cubes to model the concrete parts. We adopted the compression model in refs.  56 , 57 to simulate the behaviour of concrete under compression. Three specific parameters are required to define the response envelope: the initial elastic modulus, the fracture parameter and the compressive plastic strain. For the behaviour in tension, the spring stiffness is assumed to be linear (with the initial elastic modulus) until reaching the cracking point. The shear behaviour is considered to remain linear up to the cracking of the concrete. The interaction between normal compressive and shear stress follows the Mohr–Coulomb failure criterion. After reaching the peak, the shear stress is assumed to drop to a certain residual value affected by the aggregate interlock and friction at the cracked surface. By contrast, under tension, both normal and shear stresses drop to zero after the cracking point. The steel reinforcement bars were simulated as a discrete spring element with three force components: the normal spring takes the principal/normal forces parallel to the rebar, and two other springs represent the reinforcement bar in shear (dowelling). Three distinct stages are considered: elastic, yield plateau and strain hardening. A perfect bond behaviour between the concrete and the reinforcement bars was adopted. We assigned the material properties based on the results of the laboratory tests performed on reinforcement bars and concrete cylinders (Supplementary Information Section 2 ).

Boundary conditions and loading protocol

We assumed that all the ground floor columns are fully restrained in all six degrees of freedom at the base location. This assumption is reasonable, as we expected that the footing would provide sufficient rigidity to constrain any significant deformations. We assigned the reflecting domain boundaries to allow a realistic representation of the collapsing elements (debris) that might fall and rebound after hitting the ground. The ground level was assumed to be at the same elevation at which the column bases are restrained. We applied the additional imposed uniform distributed load as an extra volume of mass assigned to the slabs. To perform the column removal, we used the element removal feature that allows some specific designated elements to be immediately removed at the beginning of the loading stage. This represents a dynamic (sudden) removal, as we expected from the actual test.

Extended Data Tables 1 and 2 summarize all key parameters and assumptions adopted in the modelling process. To validate these assumptions for simulating the precast building designs described previously, it was ensured that the full-scale test performed as part of this work captured all relevant phenomena influencing collapse (large displacements, fracture, contact and collision).

Experiment and monitoring design

We used computational simulations of design H subjected to different initial failure scenarios to define a suitable testing sequence and protocol. The geometry, reinforcement configurations, connection system and construction details of the purpose-built specimen representing design H are provided in Supplementary Information Section 1 and Supplementary Video  4 .

Initial failure scenarios

Initial failure scenarios occurring in edge and corner regions of the building were prioritized for this study because they are usually exposed to a wider range of external threats 58 , 59 , 60 , 61 . After performing a systematic sensitivity study, we identified three critical scenarios (Extended Data Fig. 5 and Supplementary Video  2 ):

Scenario 1: a scenario involving a two-column failure—a corner column and the adjacent edge column. We determined that the required gravity loads to induce collapse equal 11.5 kN m −2 and that partial collapse would occur locally.

Scenario 2: a scenario involving a three-column failure—two corner columns and the edge column in between the two corner columns. We determined that the required gravity loads to induce collapse equal 8.5 kN m −2 and that segmentation (partially collapsing two bays) would take place only across one principal axis of the building.

Scenario 3: a scenario involving a three-column failure: one corner column and two edge columns on both sides of the corner column. We determined that the required gravity loads to induce collapse equal 7.0 kN m −2 and that segmentation (partially collapsing three bays) would take place across both principal axes of the building.

Scenario 3 was ultimately chosen after considering three main aspects: (1) it requires the lowest gravity loads to trigger partial collapse; (2) the failure mode involves activating segmentation mechanisms in two principal axes of the building (more realistic collapse pattern); and (3) the ratio of the area of the intact part and the collapsed part was predicted to be 50:50, leading to the largest collapse area among the three scenarios.

Testing phases

To allow us to investigate the behaviour of the building specimen under small and large initial failures in only one building specimen, we decided to perform two separate testing phases. Phase 1 involved the quasi-static (gradual) removal of two edge columns (C8 and C11), whereas phase 2 involved the sudden removal of the corner column (C12) found between the columns removed in phase 1. A uniformly distributed load of 11.8  kN m −2 was applied only on the bays directly adjacent to these three columns without loading the remaining bays (Supplementary Video  5 ). This was achieved by placing more than 8,000 sandbags in the designated bays on the two floors (the first- and second-floor slabs). We performed additional computational simulations to compare this partial loading configuration and loading of the entire building. The simulations indicated that both would have resulted in almost identical final collapse states (Extended Data Fig. 7 and Supplementary Video  3 ). However, the partial loading configuration introduced a higher magnitude of unbalanced moment to surrounding columns, which induces more demanding bending and shear in columns. Simulations confirmed that the lateral drift of the remaining part of the building would be higher when only three bays are loaded, indicating that its stability would be tested to a greater extent with this loading configuration (Extended Data Fig. 7 ).

Specially designed elements to trigger initial failures

We designed special devices to perform the column removal (Extended Data Fig. 6 ). For phase 1, we constructed two hanging concrete columns (C8 and C11) supported only on a vertical hydraulic jack. The pressure in the jack could be gradually released from a safe distance to remove the vertical reaction supporting the column. In phase 2, a three-steel-hinged column was used as the corner column. The middle part of the column represents a central hinge that was able to rotate if unlocked. During the second testing phase, we unlocked the hinge by pulling the column from outside the building using a forklift to induce a slight destabilization. This resulted in a sudden removal of the corner column C12 and the initiation of the collapse.

Monitoring plan

To monitor the structural behaviour, we heavily instrumented the building specimen with multiple sensors. A total of 57 embedded strain gauges, 17 displacement transducers and 5 accelerometers were placed at key locations in different parts of the structure (Extended Data Fig. 8 and Supplementary Information Section 3 ) during all phases of testing. The data from these sensors (Supplementary Information Sections 4 and 5 ) were complemented by the pictures and videos of the structural response captured by five high-resolution cameras and two drones (Supplementary Videos  6 and 8 ).

Data availability

All experimental data recorded during testing of the full-scale building are available from Zenodo ( https://doi.org/10.5281/zenodo.10698030 ) 62 . Source data are provided with this paper.

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Acknowledgements

This article is part of a project (Endure) that has received funding from the European Research Council (ERC) under the Horizon 2020 research and innovation programme of the European Union (grant agreement no. 101000396). We acknowledge the assistance of the following colleagues from the ICITECH-UPV institute in preparing and executing the full-scale building tests: J. J. Moragues, P. Calderón, D. Tasquer, G. Caredda, D. Cetina, M. L. Gerbaudo, L. Marín, M. Oliver and G. Sempértegui. We are also grateful to the Levantina, Ingeniería y Construcción S.L. (LIC) company for providing human resources and access to their facilities for testing. Finally, we thank A. Elfouly and Applied Science International for their support in performing simulations.

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Nirvan Makoond, Andri Setiawan, Manuel Buitrago & Jose M. Adam

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N.M. prepared the main text, performed the computational simulations and validated the test results. A.S. analysed the experimental data, performed data curation and prepared the Methods section. M.B. contributed to the design of the building specimen, the design of the test and data curation. J.M.A. contributed to the design of the research methodology, supervised the research and was responsible for funding acquisition. N.M., A.S. and M.B. contributed to the execution of the experimental test and to preparing figures, extended data and supplementary information. All authors interpreted the test and simulation results and edited the paper.

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Correspondence to Jose M. Adam .

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Extended data figures and tables

Extended data fig. 1 summary of building designs..

General building layout, connection details, and reinforcement configurations of Design H (“Hierarchy-based”) and Design C (“Conventional”).

Extended Data Fig. 2 Comparison of measured experimental data and simulation predictions.

a, Location of shown comparisons. All data shown in panels b to d refer to the change in structural response following the sudden removal of column C12 (after having removed columns C8 and C11 in a previous phase). b, Change in axial load in lower part of column C7. c, Change in axial load in lower part of column C9. d , Change in drift measured in both directions parallel to each building side.

Extended Data Fig. 3 Computational simulations of Design H and Design C subjected to small initial failures.

Principal strains and relative vertical displacement at the location of column C11 after removal of columns C8 and C11 from Design H ( a ) and Design C ( b ).

Extended Data Fig. 4 Demand and capacity envelopes of internal forces in Designs H and C subjected to large initial failures.

Evolution of axial loads, bending moments, and shear forces in column C7 compared to lower and upper bounds of its capacity after the removal of columns C8, C11, and C12 from Design H ( a ) and Design C ( b ).

Extended Data Fig. 5 Initial failure scenarios considered for testing.

Simulation of three different initial failure scenarios that were considered for testing. Scenario 3 was selected for the experimental test.

Extended Data Fig. 6 Specially designed removable supports to perform column removals.

Removable supports designed for quasi-static column removals in phase 1 and sudden column removal in phase 2.

Extended Data Fig. 7 Comparison of simulations of fully loaded and partially loaded building specimen.

a, Loaded bays, deformed shape, and principal normal strains following the sudden removal of column C12 (after having removed columns C8 and C11 in a previous phase). b, Horizontal displacement in the east-west and north-south directions at the top of columns C1 and C9 (2nd floor).

Extended Data Fig. 8 Measured redistribution of column axial forces during phase 1.

Maximum change in axial load of columns during phase 1 of testing based on recorded strain measurements.

Supplementary information

Supplementary information.

This file contains a supplementary test report that covers as-built building design, material properties, monitoring plan, structural response in phase 1 of testing and structural response in phase 2 of testing.

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Supplementary video 1.

Structural response of designs H and C.

Supplementary Video 2

Initial failure scenarios.

Supplementary Video 3

Comparison of partial and full loading.

Supplementary Video 4

Construction of the building.

Supplementary Video 5

An aerial view of the building before the test.

Supplementary Video 6

Multiple perspectives of the partial collapse of the building specimen in testing phase 2.

Supplementary Video 7

Experimental and simulation comparison of the partial collapse in testing phase 2.

Supplementary Video 8

Post-collapse inspection drone video.

Source data

Source data fig. 3, source data fig. 4, source data extended data fig. 2, source data extended data fig. 3, source data extended data fig. 4, rights and permissions.

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Makoond, N., Setiawan, A., Buitrago, M. et al. Arresting failure propagation in buildings through collapse isolation. Nature 629 , 592–596 (2024). https://doi.org/10.1038/s41586-024-07268-5

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Received : 07 December 2023

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DOI : https://doi.org/10.1038/s41586-024-07268-5

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2024 Best Doctoral Dissertation Advances Geotechnical Earthquake Engineering, Seismic Design

• by Molly Bechtel
• May 21, 2024

Sumeet Kumar Sinha is this year's recipient of the University of California, Davis, College of Engineering Zuhair A. Munir Award for Best Doctoral Dissertation. The award recognizes the methods, findings and significance of Sinha's research, which featured several first-of-its-kind approaches and analyses in the field of geotechnical earthquake engineering and is actively informing seismic design practices.   

The college established the annual award in 1999 in honor of Zuhair A. Munir, the former dean of engineering who led the college from 2000 to 2002 and acted as associate dean for graduate studies for 20 years. The award recognizes a doctoral student, their exemplary research and the mentorship of their major professor.  

A two-time Aggie alum, Sinha received his master's degree in 2017 and Ph.D. in 2022 from the Department of Civil and Environmental Engineering, where he was mentored by Associate Professor Katerina Ziotopoulou and Professor Emeritus Bruce Kutter . He is now an assistant professor in the Department of Civil Engineering at the Indian Institute of Technology Delhi and co-founder of BrahmaSens, a startup that specializes in the development of sensing technologies and solutions for application in various sectors including health-monitoring of civil infrastructures.  

"It's really a special honor to get this [award]," said Sinha. "It acknowledges both the depth and significance of the research I conducted during my Ph.D."   

Sinha's dissertation is of notable significance in California, where agencies like the Department of Transportation, or Caltrans, which funded his research, are eager to identify improved design methods in seismically active regions of the state.  

In " Liquefaction-Induced Downdrag on Piles: Centrifuge and Numerical Modeling, and Design Procedures ," Sinha focuses on the effects of earthquakes on deep foundations, like piles, in soils that can liquefy. Liquefaction occurs when wet sand-like soils lose their strength due to increased pore water pressure during earthquake shaking. This causes the soil to behave like a liquid, leading to significant ground deformations.   

After the shaking stops, the soil slowly regains its strength as the water drains out, but this settling and densifying process, called reconsolidation, can drag down piles downward. Additional downdrag loads have not always been properly accounted for in conventional design.   

Through centrifuge model tests at the UC Davis Center for Geotechnical Modeling , Sinha developed numerical models to evaluate scenarios. His findings include procedures for accurately estimating downdrag loads and the corresponding demands on pile foundations, as well as practical methods to design bridges in a more efficient and economical way.  

"Dr. Sinha's methods, approaches, documentation, results and overall findings have been, by any standards, novel and meticulous," said Ziotopoulou in her nomination letter. "His research represents a significant and original contribution to the field of geotechnical earthquake engineering, and his findings have already been implemented into practice by major design firms."  

Sinha's research was recognized with a DesignSafe Dataset Award , an Editor's Choice in his field's top journal and the Michael Condon Scholarship from the Deep Foundations Institute. He has published seven papers in peer-reviewed journals.  

Of perhaps greater meaning to Sinha is making improvements in the design codes to make them more informed, feasible, economical, resilient and sustainable through the complete understanding of the mechanism obtained through his findings from experiments, developed numerical models and design procedures, which are available publicly via platforms such as GitHub and DesignSafe.   

"My philosophy has always been to convert whatever I'm doing into a product, a tool which has a wider impact," explained Sinha. "During my Ph.D., I tried to go beyond the deliverables so that I maximize the impact of [my research]."  

Sinha is grateful for his mentors' and peers' influence and support during the five-year Ph.D. program at UC Davis.  

"I have learned a lot from [Professors Katerina Ziotopoulou and Bruce Kutter] academically as well as professionally," said Sinha. "The Geotechnical Graduate Student Society also had a very important role in my overall experience at UC Davis."  

Primary Category

Quenching Distance of Premixed Jet-A/Air Mixtures

Quenching distance is a fundamental property of hydrocarbon fuel-air mixtures and is a crucial parameter guiding process and equipment design for fire hazard mitigation. Many industrial equipment such as flame arrestors and burners rely on the fundamental principle of flame quenching, i.e., a premixed flame cannot pass through confined spaces below a critical width, given by the Quenching Distance (QD) of the fuel-air mixture. Through the efforts spanning over more than a century, QD is found to depend on various parameters such as temperature, pressure, fuel-air equivalence ratio, and the characteristics of hydrocarbons comprising the fuel. Many investigations on flame quenching behavior have focused on simple fuels such as Hydrogen, Methane, and hydrocarbons upto n-Decane. However, there is a lack of quenching distance data on aviation fuels like Jet-A likely due to the fact that QD property of these fuels is less relevant in practical combustor applications. But in this era of miniaturization, there are several upcoming technologies that will utilize jet fuels or kerosene in confined spaces. For example, a recently proposed Printed Circuit Heat Exchanger (PCHE) is being considered for jet engine performance enhancement by cooling down the compressor discharge air using fuel prior to injection. The cooled air can be used to improve turbine cooling allowing for improvement of the thermal efficiency of the jet engine. However, a major cause of concern during the PCHE operation is the accidental internal fuel leakage from high pressure fuel microchannels into the surrounding air microchannels. Under the severe operating conditions of a jet engine (T >800K, P >10bar), the leaking fuel upon mixing with air pose ignition and sustained combustion risks. This must be evaluated against the competing phenomenon of flame arrestment, since the channel sizes in PCHEs are very small (in the order of a few hundred micrometers). Thus, it becomes imperative to measure the quenching distance of jet fuels to design the microscale passages, predict and mitigate fire hazards to ensure safe operation.

In the present work, the quenching distance of homogeneous, quiescent Jet-A/air mixtures at 473K, 1atm under various equivalence ratios (lean to rich) have been studied. For this purpose, experiments were setup using the ASTM Standard Method that involves using flanged electrodes to measure the parallel-plate QD of quiescent, pre-vaporized fuel-air mixtures under various conditions. Validation tests were carried out with Methanol/air mixtures at 373K, 1atm for different equivalence ratios. For tests with Jet-A/air mixtures, the QD variation with equivalence ratio follows similar trends as that of n-Decane/air. On further analyzing the QD variation with equivalence ratio, we see that the QD minimizes on fuel rich conditions with increasing molecular weight of the fuel which is consistent with the trend shown in literature. The flame propagation behavior shows considerable differences on the lean and the rich sides.

Moreover, the quenching distance of quiescent Methanol/air and Jet-A/air mixtures have been estimated using three different models taken from literature. Model parameters were calculated using Chemkin Pro simulations of the premixed flames at the similar initial conditions as the experiments. On comparing the experiment data with model predictions, we observe that the models agree well with experiment data for Methanol/air mixtures, whereas they fail to capture the QD variation with equivalence ratio for Jet-A/air mixtures. The disagreement may arise because of the high molecular weight of Jet-A that causes the Lewis number to be non-unity unlike Methanol/air mixtures. Therefore, an empirical power law relation has been developed for estimating the QD of hydrocarbon/air mixtures to the incorporate the Lewis number effect. The model agrees well with Jet-A/air QD data from experiments over the entire equivalence ratios. This will help to further our understanding of the complex fuel combustion and flame quenching for better risk mitigation.

Degree Type

• Master of Science
• Aeronautics and Astronautics

Campus location

• West Lafayette

Advisor/Supervisor/Committee Chair

Additional committee member 2, additional committee member 3, usage metrics.

• Aerospace engineering not elsewhere classified
• Automotive combustion and fuel engineering