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.
Examples •
Male and female: An experiment is designed to test a new drug on patients. There are two levels of the treatment,
drug, and
placebo, administered to
male and
female patients in a
double blind trial. The sex of the patient is a
blocking factor accounting for treatment variability between
males and
females. This reduces sources of variability and thus leads to greater precision. •
Elevation: An experiment is designed to test the effects of a new pesticide on a specific patch of grass. The grass area contains a major elevation change and thus consists of two distinct regions – 'high elevation' and 'low elevation'. A treatment group (the new pesticide) and a placebo group are applied to both the high elevation and low elevation areas of grass. In this instance the researcher is blocking the elevation factor which may account for variability in the pesticide's application. •
Intervention: Suppose a process is invented that intends to make the soles of shoes last longer, and a plan is formed to conduct a field trial. Given a group of
n volunteers, one possible design would be to give
n/2 of them shoes with the new soles and
n/2 of them shoes with the ordinary soles,
randomizing the assignment of the two kinds of soles. This type of experiment is a
completely randomized design. Both groups are then asked to use their shoes for a period of time, and then measure the degree of wear of the soles. This is a workable experimental design, but purely from the point of view of statistical accuracy (ignoring any other factors), a better design would be to give each person one regular sole and one new sole, randomly assigning the two types to the left and right shoe of each volunteer. Such a design is called a "randomized complete
block design." This design will be more sensitive than the first, because each person is acting as his/her own control and thus the
control group is more closely matched to the
treatment group block design
Nuisance variables 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.
Blocking used for nuisance factors that can be controlled 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. When studying probability theory the blocks method consists of splitting a sample into blocks (groups) separated by smaller subblocks so that the blocks can be considered almost independent. The blocks method helps proving limit theorems in the case of dependent random variables. The blocks method was introduced by
S. Bernstein: The method was successfully applied in the theory of sums of dependent random variables and in
extreme value theory.
Example In our previous diet pills example, a blocking factor could be the sex of a patient. We could put individuals into one of two blocks (male or female). And within each of the two blocks, we can randomly assign the patients to either the diet pill (treatment) or placebo pill (control). By blocking on sex, this source of variability is controlled, therefore, leading to greater interpretation of how the diet pills affect weight loss.
Definition of blocking factors A nuisance factor is used as a blocking factor if every level of the primary factor occurs the same number of times with each level of the nuisance factor. == Implementation ==