In statistics, a collection of random variables is heteroscedastic (often spelled heteroskedastic,[1] and commonly pronounced with a hard k 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').

Suppose there is a sequence of random variables {Yt}t=1n and a sequence of vectors of random variables, {Xt}t=1n. In dealing with conditional expectations of Yt given Xt, the sequence {Yt}t=1n is said to be heteroskedastic if the conditional variance of Yt given Xt, changes with t. Some authors refer to this as conditional heteroscedasticity to emphasize the fact that it is the sequence of conditional variances that changes and not the unconditional variance. In fact it is possible to observe conditional heteroscedasticity even when dealing with a sequence of unconditional homoscedastic random variables, however, the opposite does not hold. If the variance changes only because of changes in value of X and not because of a dependence on the index t, the changing variance might be described using a scedastic function.

When using some statistical techniques, such as ordinary least squares (OLS), a number of assumptions are typically made. One of these is that the error term has a constant variance. This might not be true even if the error term is assumed to be drawn from identical distributions.

For example, the error term could vary or increase with each observation, something that is often the case with cross-sectional or time series measurements. Heteroscedasticity is often studied as part of econometrics, which frequently deals with data exhibiting it. White's influential paper[2] used "heteroskedasticity" instead of "heteroscedasticity" whereas the latter has been used in later works.[3]