# Homogeneity (statistics)

**homogeneityhomogeneousheterogeneityHeterogeneity (statistics)Heterogeneity in statisticsheterogeneousheterogeneous durationsheterogenicstatistical heterogeneitystatistical homogeneity**

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

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### Study heterogeneity

**heterogeneitysystematic 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).

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

### Meta-analysis

**meta-analysesmeta analysismeta-analytic**

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

### Homoscedasticity

**homoscedastichomogeneity of variancehomoskedastic**

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

### Statistics

**statisticalstatistical analysisstatistician**

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

### Data set

**datasetdatasetsdata sets**

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

### Variance

**sample variancepopulation variancevariability**

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

### Empirical distribution function

**statistical distributionempirical distributiondistribution**

However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter.

### Location parameter

**locationlocation modellocation parameters**

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.

### Marginal distribution

**marginal probabilitymarginalmarginals**

Thus, a more detailed study would examine changes to the whole of the marginal distribution.

### Skewness

**skewedskewskewed distribution**

An intermediate-level study might move from looking at the variability to studying changes in the skewness.

### Joint probability distribution

**joint distributionjoint probabilitymultivariate distribution**

In addition to these, questions of homogeneity apply also to the joint distributions.

### Regression analysis

**regressionmultiple regressionregression model**

See regression analysis.

### Hydrology

**hydrologicalhydrologisthydrologic**

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

### Meteorology

**meteorologicalmeteorologistmeteorologists**

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.

### Statistical population

**populationsubpopulationsubpopulations**

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

### Energy distance

**E-statisticE-statisticsEnergy statistics**

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

### Location test

**Comparing meansone-sample location testtests of location**

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

### Homogeneity and heterogeneity

**heterogeneoushomogeneousheterogeneity**

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

### Continuum mechanics

**continuumcontinuous mediacontinuum physics**

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.

### Coherent risk measure

**convex risk measurecoherentconvex and coherent risk measurement**

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

### Linear trend estimation

**trendTrend estimationtrends**

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

### Markov switching multifractal

**regime-switching**

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.

### Pearson's chi-squared test

**chi-square statisticPearson chi-squared testchi-square**