In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. In meta-analysis, which combines data from any number of studies, homogeneity measures the differences or similarities between those studies' (see also study heterogeneity) estimates.

Homogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of statistical distributions, including the location parameter. Thus, a more detailed study would examine changes to the whole of the marginal distribution. An intermediate-level study might move from looking at the variability to studying changes in the skewness. In addition to these, questions of homogeneity also apply to the joint distributions.

The concept of homogeneity can be applied in many different ways. For certain types of statistical analysis, it is used to look for further properties that might need to be treated as varying within a dataset once some initial types of non-homogeneity have been dealt with.

In statistics, a sequence of random variables is homoscedastic (/ˌhoʊmoʊskəˈdæstɪk/) if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings homoskedasticity and heteroskedasticity are also frequently used. “Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”. Assuming a variable is homoscedastic when in reality it is heteroscedastic (/ˌhɛtəroʊskəˈdæstɪk/) results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient.

The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance that assume that the modelling errors all have the same variance. While the ordinary least squares (OLS) estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and inference based on the assumption of homoskedasticity is misleading. In that case, generalized least squares (GLS) was frequently used in the past. Nowadays, standard practice in econometrics is to include Heteroskedasticity-consistent standard errors instead of using GLS, as GLS can exhibit strong bias in small samples if the actual skedastic function is unknown.

Because heteroscedasticity concerns expectations of the second moment of the errors, its presence is referred to as misspecification of the second order.

Differences in the typical values across the dataset might initially be dealt with by constructing a regression model using certain explanatory variables to relate variations in the typical value to known quantities. There should then be a later stage of analysis to examine whether the errors in the predictions from the regression behave in the same way across the dataset. Thus, the question becomes one of the homogeneity of the distribution of the residuals, as the explanatory variables change. See regression analysis.

The initial stages in analyzing a time series may involve plotting values against time to examine the series' homogeneity in various ways: stability across time as opposed to a trend, stability of local fluctuations over time.