Categories → Causal Inference , Statistics , Variables , Independence
In statistics, independence refers to the lack of a relationship or dependence between two or more variables.
In statistics, independence refers to the lack of association between two variables, or two samples. When two variables are independent, the value of one variable does not influence the value of the other variable. Similarly, when two samples are independent, the values in one sample are not related to and were not affected by the values in the other sample.
Independence is important in statistics because many statistical tests and models assume independence between variables or samples. If there is a dependence between variables or samples, the statistical tests or models may give incorrect results. Therefore, it is essential to check for independence before performing statistical analyses.
In terms of samples, independence means that the observations in one sample are not related to the observations in another sample. For example, if we are comparing the heights of men and women, we need to ensure that the men and women are independent samples. If the samples are not independent, such as if we are comparing the heights of husbands and wives, the statistical analysis may be biased.
In terms of variables, independence means that the values of one variable do not affect the values of another variable. For example, if we are studying the relationship between height and weight, we need to ensure that height and weight are independent variables. If there is a relationship between height and weight, the statistical analysis may be biased.
Independence is also important in causal inference. Causal inference is the process of determining whether a cause-and-effect relationship exists between two variables. If two variables are independent, it is unlikely that there is a cause-and-effect relationship between them. However, if two variables are dependent, it is possible that one variable causes the other variable.
Independence can be represented in a causal diagram by an absence of arrows (a directed path) between the variables. In a causal diagram, an arrow from variable A to variable B indicates that A directly causes B (the effect may be arbitrarily small or insignificant). If there is no arrow (or directed path) between variables A and B, they must be independent - or the causal diagram is incorrect.
It may be surprising that statistical independence does not prove the absence of a causal relationship. This example shows how directed paths can cancel each other out.