Homogeneity (statistics)

In meta-analysis, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity).

When this excessive variation occurs, it is called statistical heterogeneity, or just heterogeneity.

In meta-analysis, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity).

For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset.

In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets.

In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets.

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 the statistical distributions, including the location parameter.

However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter. A location test tests the simpler hypothesis that distributions have the same 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 apply also to the joint distributions.

See regression analysis.

In hydrology, data-series across a number of sites composed of annual values of the within-year annual maximum river-flow are analysed.

In meteorology, weather datasets are acquired over many years of record and, as part of this, measurements at certain stations may cease occasionally while, at around the same time, measurements may start at nearby locations.

Assessing the homogeneity of the population would involve looking to see whether the responses of certain identifiable subpopulations differ from those of others.

A test for homogeneity, in the sense of exact equivalence of statistical distributions, can be based on an E-statistic.

A location test tests the simpler hypothesis that distributions have the same location parameter.

*Homogeneity and heterogeneity describes uses of this terminology in wider contexts

The validity of the continuum assumption may be verified by a theoretical analysis, in which either some clear periodicity is identified or statistical homogeneity and ergodicity of the microstructure exists.

A coherent risk measure is a function \varrho that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance.

In the latter case, issues of homogeneity are important (for example, about whether the series is equally reliable throughout its length).

In financial econometrics, the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fisher that incorporates stochastic volatility components of heterogeneous durations.