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Concept
Blocking (statistics)
Summary
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). Blocking can be used to tackle the problem of pseudoreplication.
Blocking reduces unexplained variability. Its principle lies in the fact that variability which cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is confounded or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product. High order interactions are usually of the least importance (think of the fact that temperature of a reactor or the batch of raw materials is more important than the combination of the two – this is especially true when more (3, 4, ...) factors are present); thus it is preferable to confound this variability with the higher interaction.
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.
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Statistical unit
In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a "random variable". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied. Units are often referred to as being either experimental units, sampling units or units of observation: An "experimental unit" is typically thought of as one member of a set of objects that are initially equal, with each object then subjected to one of several experimental treatments.
Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids.
Interaction (statistics)
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive). Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations (then also called moderation or effect modification).