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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. Thus, a more detailed study would examine changes to the whole of the marginal distribution.
In statistics, (between-) study heterogeneity is a phenomenon that commonly occurs when attempting to undertake a meta-analysis. In a simplistic scenario, studies whose results are to be combined in the meta-analysis would all be undertaken in the same way and to the same experimental protocols.
Upon observing variation among all data points, for instance via a histogram, "probability may be used to describe such variation". [4] Let us hence denote by Y i j k {\displaystyle Y_{ijk}} the random variable which observed value y i j k {\displaystyle y_{ijk}} is the k {\displaystyle k} -th measure for treatment ( i , j ) {\displaystyle (i,j)} .
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
Most meta-analyses include between 2 and 4 studies and such a sample is more often than not inadequate to accurately estimate heterogeneity. Thus it appears that in small meta-analyses, an incorrect zero between study variance estimate is obtained, leading to a false homogeneity assumption.
[2] A 2009 study in developmental psychology examined non-cognitive traits including blood parameters and birth weight as well as certain cognitive traits, and concluded that "greater intrasex phenotype variability in males than in females is a fundamental aspect of the gender differences in humans". [19]
The main disadvantage with between-group designs is that they can be complex and often require a large number of participants to generate any useful and reliable data. For example, researchers testing the effectiveness of a treatment for severe depression might need two groups of twenty patients for a control and a test group. If they wanted to ...
In statistics, Bartlett's test, named after Maurice Stevenson Bartlett, [1] is used to test homoscedasticity, that is, if multiple samples are from populations with equal variances. [2] Some statistical tests, such as the analysis of variance , assume that variances are equal across groups or samples, which can be checked with Bartlett's test.