# 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