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The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. He described how to test the hypothesis that a certain lady could distinguish by flavor alone whether the milk or the tea was first placed in the cup. While this sounds like a frivolous application, it allowed him to illustrate the most important means of experimental design:
- Randomization - The process of making something random
- Replication - repeating the creation of a phenomenon, so that the variability associated with the phenomenon can be estimated
- Blocking - the arranging of experimental units in groups (blocks) which are similar to one another
- Orthogonality - Means perpendicular, at right angles or statistically normal.
- Use of factorial experiments instead of the one-factor-at-a-time method
Analysis of the design of experiments was built on the foundation of the analysis of variance, a collection of models in which the observed variance is partitioned into components due to different factors which are estimated and/or tested.
Some efficient designs for estimating several main effects simultaneously were found by Raj Chandra Bose and K. Kishen in 1940 at the Indian Statistical Institute, but remained little known until the Plackett-Burman designs were published in Biometrika in 1946.
As with all other branches of statistics, there is both classical and Bayesian experimental design.
The weights of eight objects are to be measured using a pan balance that measures the difference between the weight of the objects in the two pans. Each measurement has a random error. The average error is zero; the standard deviations of the probability distribution of the errors is the same number σ on different weighings; and errors on different weighings are independent. Denote the true weights by
We consider two different experiments:
- Weigh each object in one pan, with the other pan empty. Call the measured weight of the ith object Xi for i = 1, ..., 8.
- Do the eight weighings according to the following schedule and let Yi be the measured difference for i = 1, ..., 8:
- Then the estimated value of the weight θ1 is
The question of design of experiments is: which experiment is better?
The variance of the estimate X1 of θ1 is σ2 if we use the first experiment. But if we use the second experiment, the variance of the estimate given above is σ2/8. Thus the second experiment gives us 8 times as much precision.
Many problems of the design of experiments involve combinatorial designs, as in this example.
Types of design
Some of the most popular designs are sorted below, with the ones at the top being the most powerful at reducing observer-expectancy effect but also most expensive, and in some cases introducing ethical concerns. The ones at the bottom are the most affordable, and are frequently used earlier in the research cycle, to develop strong hypotheses worth testing with the more expensive research approaches.
- Randomized controlled trial
- Nonrandomized controlled trial
- Randomized database studies
- Cohort study
- Case-cohort study
- Case-control study (case series)
- Cross-sectional study
- Community survey
Ordering of conditions
An important aspect of some experiment designs is the ordering of different experimental conditions.
When choosing a study design, many factors must be taken into account. Different types of studies are subject to different types of bias. For example, recall bias is likely to occur in cross-sectional or case-control studies where subjects are asked to recall exposure to risk factors. Subjects with the relevant condition (e.g. breast cancer) may be more likely to recall the relevant exposures that they had undergone (e.g. hormone replacement therapy) than subjects who don't have the condition.
The ecological fallacy may occur when analyses are done on ecological (group-based) data rather than individual data. The nature of this type of analysis tends to overestimate the degree of association between variables.
- A "retrospective study" looks at past behavior, while a "prospective study" looks at future behavior.
- "Superiority trials" are designed to demonstrate that one treatment is more effective than another.
- "Non-inferiority trials" are designed to demonstrate that a treatment is at least not appreciably worse than another.
- "Equivalence trials" are designed to demonstrate that one treatment is as effective as another.
- When using "parallel groups", each patient receives one treatment; in a "crossover study", each patient receives several treatments.
- A longitudinal study studies a few subjects for a long period of time, while a cross-sectional study involves many subjects measured at once.
- Animal models
- Between groups design
- Case study in psychology
- Conjoint measurement
- Clinical trial
- Cohort analysis
- Debriefing (experimental)
- Design of experiments
- Epidemiological methods
- Experimental control
- Experimental methods
- Experiment volunteers
- Followup studies
- Hypothesis testing
- Repeated measures
- Research setting
- Sampling (experimental)
- Statistical analysis
- Statistical variables
- Test construction
- Herman Chernoff, Sequential Analysis and Optimal Design, SIAM Monograph, 1972.
- Epidemiologic.org Epidemiologic Inquiry online weblog for epidemiology researchers
- Epidemiology Forum An epidemiology discussion and forum community to foster debates and collaborations in epidemiology
- Some aspects of study design Tufts University web site
-  Truman State University Political Science Research Design Handbook
- Description of how to design experiments
- Articles on Design of Experiments
- Czitrom (1999) "One-Factor-at-a-Time Versus Designed Experiments", American Statistician, 53, 2.
- SAS Examples for Experimental Design
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Research design: Academic support materials
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Research methods: Study designs / Design of experiments
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