# Statistical unit

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A unit in a statistical analysis refers to one member of a set of entities being studied. It is the material source for the mathematical abstraction of a "random variable". Common examples of a unit would be a single person, animal, plant, or manufactured item that belongs to a larger collection of such entities being studied.

Units are often referred to as being either experimental units, sampling units or, more generally, units of observation:

• An "experimental unit" is typically thought of as one member of a set of objects that are initially equivalent, with each object then subjected to one of several experimental treatments.

In most statistical studies, the goal is to generalize from the observed units to a larger set consisting of all comparable units that exist but are not directly observed. For example, if we randomly sample 100 people and ask them which candidate they intend to vote for in an election, our main interest is in the voting behavior of all eligible voters, not exclusively on the 100 observed units.

In some cases, the observed units may not form a sample from any meaningful population, but rather constitute a convenience sample, or may represent the entire population of interest. In this situation, we may study the units descriptively, or we may study their dynamics over time. But it typically does not make sense to talk about generalizing to a larger population of such units. Studies involving countries or business firms are often of this type.

In simple data sets, the units are in one-to-one correspondence with the data values. In more complex data sets, multiple measurements are made for each unit. For example, if blood pressure measurements are made daily for a week on each subject in a study, there would be seven data values for each statistical unit.

While a unit is often the lowest level at which observations are made, in some cases, a unit can be further decomposed as a statistical assembly.

Many statistical analyses use quantitative data that have units of measurement. This is a distinct and non-overlapping use of the term "unit."