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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.
The formula for the one-way ANOVA F-test statistic is =, or =. The "explained variance", or "between-group variability" is = (¯ ¯) / where ¯ denotes the sample mean in the i-th group, is the number of observations in the i-th group, ¯ denotes the overall mean of the data, and denotes the number of groups.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences between groups.
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.
The coefficient of variation is useful because the standard deviation of data must always be understood in the context of the mean of the data. In contrast, the actual value of the CV is independent of the unit in which the measurement has been taken, so it is a dimensionless number .
Example of samples from two populations with the same mean but different dispersion. The blue population is much more dispersed than the red population. In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1]
The maximum likelihood method has many advantages in that it allows researchers to compute of a wide range of indexes of the goodness of fit of the model, it allows researchers to test the statistical significance of factor loadings, calculate correlations among factors and compute confidence intervals for these parameters. [6]
The population MAD is defined analogously to the sample MAD, but is based on the complete population rather than on a sample. For a symmetric distribution with zero mean, the population MAD is the 75th percentile of the distribution. Unlike the variance, which may be infinite or undefined, the population MAD is always a finite number.