In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks) based on one or more variables. These variables are chosen carefully to minimize the effect of their variability on the observed outcomes. There are different ways that blocking can be implemented, resulting in different confounding effects. However, the different methods share the same purpose: to control variability introduced by specific factors that could influence the outcome of an experiment. The roots of blocking originated from the statistician, Ronald Fisher, following his development of ANOVA.

The use of blocking in experimental design has an evolving history that spans multiple disciplines. The foundational concepts of blocking date back to the early 20th century with statisticians like Ronald A. Fisher. His work in developing analysis of variance (ANOVA) set the groundwork for grouping experimental units to control for extraneous variables. Blocking evolved over the years, leading to the formalization of randomized block designs and Latin square designs. Today, blocking still plays a pivotal role in experimental design, and in recent years, advancements in statistical software and computational capabilities have allowed researchers to explore more intricate blocking designs.

We often want to reduce or eliminate the influence of some Confounding factor when designing an experiment. We can sometimes do this by "blocking", which involves the separate consideration of blocks of data that have different levels of exposure to that factor.

In the examples listed above, a nuisance variable is a variable that is not the primary focus of the study but can affect the outcomes of the experiment. They are considered potential sources of variability that, if not controlled or accounted for, may confound the interpretation between the independent and dependent variables.

To address nuisance variables, researchers can employ different methods such as blocking or randomization. Blocking involves grouping experimental units based on levels of the nuisance variable to control for its influence. Randomization helps distribute the effects of nuisance variables evenly across treatment groups.

By using one of these methods to account for nuisance variables, researchers can enhance the internal validity of their experiments, ensuring that the effects observed are more likely attributable to the manipulated variables rather than extraneous influences.

In the first example provided above, the sex of the patient would be a nuisance variable. For example, consider if the drug was a diet pill and the researchers wanted to test the effect of the diet pills on weight loss. The explanatory variable is the diet pill and the response variable is the amount of weight loss. Although the sex of the patient is not the main focus of the experiment—the effect of the drug is—it is possible that the sex of the individual will affect the amount of weight lost.

In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter.