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The curve with the greater variability (green) yields higher values in both the lowest and highest ends of the range. The variability hypothesis, also known as the greater male variability hypothesis, is the hypothesis that males generally display greater variability in traits than females do.
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This is an analog of the mean difference - the average of the differences of all the possible pairs of variate values, taken regardless of sign. The mean difference differs from the mean and standard deviation because it is dependent on the spread of the variate values among themselves and not on the deviations from some central value.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance , standard deviation , and interquartile range .
A classic example of heteroscedasticity is that of income versus expenditure on meals. A wealthy person may eat inexpensive food sometimes and expensive food at other times. A poor person will almost always eat inexpensive food. Therefore, people with higher incomes exhibit greater variability in expenditures on food.
^ (): greater variability in a particular covariate leads to proportionately less variance in the corresponding coefficient estimate; The remaining term, 1 / (1 − R j 2) is the VIF. It reflects all other factors that influence the uncertainty in the coefficient estimates.
The data set [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as 10 / 100 = 0.1; The data set [1, 5, 6, 8, 10, 40, 65, 88] has still more variability. Its standard deviation is 32.9 and its average is 27.9, giving a coefficient of variation of 32.9 / 27.9 = 1.18
Reasons for the additional variability are usually differences in the studies themselves, the investigated populations, treatment schedules, endpoint definitions, or other circumstances ("clinical diversity"), or the way data were analyzed, what models were employed, or whether estimates have been adjusted in some way ("methodological diversity ...