Statistical unit
Encyclopedia
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
:
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."
Random variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
". 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
Unit of observation
The Unit of observation is the unit on which one collects data . For example, a study may have a unit of observation at the individual level but may have the unit of analysis at the neighborhood level, drawing conclusions on neighborhood characteristics from data collected from individuals....
:
- 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.
- A "sampling unit" is typically thought of as an object that has been sampled from a statistical populationStatistical populationA statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest...
. This term is commonly used in opinion polling and survey samplingSurvey samplingIn statistics, survey sampling describes the process of selecting a sample of elements from a target population in order to conduct a survey.A survey may refer to many different types or techniques of observation, but in the context of survey sampling it most often involves a questionnaire used to...
.
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
Accidental sampling
Accidental sampling is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, a sample population selected because it is readily available and convenient...
, or may represent the entire population of interest. In this situation, we may study the units descriptively
Descriptive statistics
Descriptive statistics quantitatively describe the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics , in that descriptive statistics aim to summarize a data set, rather than use the data to learn about the population that the data are...
, 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
Country
A country is a region legally identified as a distinct entity in political geography. A country may be an independent sovereign state or one that is occupied by another state, as a non-sovereign or formerly sovereign political division, or a geographic region associated with a previously...
or business firms
Business
A business is an organization engaged in the trade of goods, services, or both to consumers. Businesses are predominant in capitalist economies, where most of them are privately owned and administered to earn profit to increase the wealth of their owners. Businesses may also be not-for-profit...
are often of this type.
In simple data
Data
The term data refers to qualitative or quantitative attributes of a variable or set of variables. Data are typically the results of measurements and can be the basis of graphs, images, or observations of a set of variables. Data are often viewed as the lowest level of abstraction from which...
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
Statistical assembly
In statistics, for example in statistical quality control, a statistical assembly is a collection of parts or components which makes up a statistical unit. Thus a statistical unit, which would be the prime item of concern, is made of discrete components like organs or machine parts...
.
Many statistical analyses use quantitative data
Data
The term data refers to qualitative or quantitative attributes of a variable or set of variables. Data are typically the results of measurements and can be the basis of graphs, images, or observations of a set of variables. Data are often viewed as the lowest level of abstraction from which...
that have units of measurement
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...
. This is a distinct and non-overlapping use of the term "unit."