Experimental Design

In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. Formal planned experimentation is often used in evaluating physical objects, chemical formulations, structures, components, and materials. In the design of experiments, the experimenter is often interested in the effect of some process or intervention (the "treatment") on some objects (the "experimental units"), which may be people, parts of people, groups of people, plants, animals, etc. Design of experiments is thus a discipline that has very broad application across all the natural and social sciences and engineering.

A methodology for designing experiments was proposed by Ronald A. Fisher in his innovative books The Arrangement of Field Experiments (1926) and The Design of Experiments (1935). These methods have been broadly adapted in the physical and social sciences.

Old-fashioned scale

A scale is emblematic of the methodology of experimental design which includes comparison, replication, and factorial considerations.

• Comparison: In some fields of study it is not possible to have independent measurements to a traceable standard. Comparisons between treatments are much more valuable and are usually preferable. Often one compares against a scientific control or traditional treatment that acts as baseline.
• Randomization: Random assignment is the process of assigning individuals at random to groups or to different groups in an experiment. The random assignment of individuals to groups (or conditions within a group) distinguishes a rigorous, "true" experiment from an adequate, but less-than-rigorous, "quasi-experiment". Random does not mean haphazard, and great care must be taken that appropriate random methods are used.
• Replication: Measurements are usually subject to variation and uncertainty. Measurements are repeated and full experiments are replicated to help identify the sources of variation, to better estimate the true effects of treatments, to further strengthen the experiment's reliability and validity, and to add to the existing knowledge of the topic.
• Blocking: Blocking is the arrangement of experimental units into groups (blocks) consisting of units that are similar to one another. Blocking reduces known but irrelevant sources of variation between units and thus allows greater precision in the estimation of the source of variation under study.
• Orthogonality: Orthogonality concerns the forms of comparison (contrasts) that can be legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal. Because of this independence, each orthogonal treatment provides different information to the others. If there are $T$ treatments and $T-1$ orthogonal contrasts, all the information that can be captured from the experiment is obtainable from the set of contrasts.
• Factorial experiments: Use of factorial experiments instead of the one-factor-at-a-time method. These are efficient at evaluating the effects and possible interactions of several factors (independent variables). Analysis of experiment design is built on the foundation of the analysis of variance, a collection of models that partition the observed variance into components, according to what factors the experiment must estimate or test.

It is best that a process be in reasonable statistical control prior to conducting designed experiments. When this is not possible, proper blocking, replication, and randomization allow for the careful conduct of designed experiments. To control for nuisance variables, researchers institute control checks as additional measures. Investigators should ensure that uncontrolled influences (e.g., source credibility perception) are measured do not skew the findings of the study.

One of the most important requirements of experimental research designs is the necessity of eliminating the effects of spurious, intervening, and antecedent variables. In the most basic model, cause ($X$) leads to effect ($Y$). But there could be a third variable ($Z$) that influences ($Y$), and $X$ might not be the true cause at all. $Z$ is said to be a spurious variable and must be controlled for. The same is true for intervening variables (a variable in between the supposed cause ($X$) and the effect ($Y$)), and anteceding variables (a variable prior to the supposed cause ($X$) that is the true cause). In most designs, only one of these causes is manipulated at a time.