Heteroscedasticity

Heteroscedasticity

In statistics, a collection of random variables is heteroscedastic (often spelled heteroskedastic, and commonly pronounced with a hard k sound regardless of spelling) if there are sub-populations that have different variabilities from others. Here "variability" could be quantified by the variance or any other measure of statistical dispersion. Thus heteroscedasticity is the absence of homoscedasticity.

The possible existence of heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, because the presence of heteroscedasticity can invalidate statistical tests of significance that assume that the modelling errors are uncorrelated and normally distributed and that their variances do not vary with the effects being modelled. Similarly, in testing for differences between sub-populations using a location test, some standard tests assume that variances within groups are equal.

Tests for the possible presence of heteroscedasticity are outlined below.

The term means "differing variance" and comes from the Greek "hetero" ('different') and "skedasis" ('dispersion').