Association (statistics)
Encyclopedia
In statistics
, an association is any relationship between two measured quantities that renders them statistically dependent. The term "association" refers broadly to any such relationship, whereas the narrower term "correlation
" refers to a linear relationship between two quantities.
There are many statistical measures of association that can be used to infer the presence or absence of an association in a sample of data
. Examples of such measures include the product moment correlation coefficient, used mainly for quantitative measurements, and the odds ratio
, used for dichotomous measurements. Other measures of association are the distance correlation
, tetrachoric correlation coefficient, Goodman and Kruskal's lambda
, Tschuprow's T
and Cramér's V
In quantitative research, the term "association" is often used to emphasize that a relationship being discussed is not necessarily causal
(see correlation does not imply causation
).
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, an association is any relationship between two measured quantities that renders them statistically dependent. The term "association" refers broadly to any such relationship, whereas the narrower term "correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
" refers to a linear relationship between two quantities.
There are many statistical measures of association that can be used to infer the presence or absence of an association in a sample of 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...
. Examples of such measures include the product moment correlation coefficient, used mainly for quantitative measurements, and the odds ratio
Odds ratio
The odds ratio is a measure of effect size, describing the strength of association or non-independence between two binary data values. It is used as a descriptive statistic, and plays an important role in logistic regression...
, used for dichotomous measurements. Other measures of association are the distance correlation
Distance correlation
In statistics and in probability theory, distance correlation is a measure of statistical dependence between two random variables or two random vectors of arbitrary, not necessarily equal dimension. Its important property is that this measure of dependence is zero if and only if the random...
, tetrachoric correlation coefficient, Goodman and Kruskal's lambda
Goodman and Kruskal's lambda
In probability theory and statistics, Goodman & Kruskal's lambda is a measure of proportional reduction in error in cross tabulation analysis...
, Tschuprow's T
Tschuprow's T
In statistics, Tschuprow's T is a measure of association between two nominal variables, giving a value between 0 and 1 . It is closely related to Cramér's V, coinciding with it for square contingency tables....
and Cramér's V
In quantitative research, the term "association" is often used to emphasize that a relationship being discussed is not necessarily causal
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
(see correlation does not imply causation
Correlation does not imply causation
"Correlation does not imply causation" is a phrase used in science and statistics to emphasize that correlation between two variables does not automatically imply that one causes the other "Correlation does not imply causation" (related to "ignoring a common cause" and questionable cause) is a...
).