You may overide this value.">Effect size value
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The Levene's test checks if the difference between the variability of two or more groups is significant.
The Levene's test doesn't compare the variances, but compare the Mean Absolute Deviations (MAD), which is another way to check the data variability, on the other hand if the MADs are not the same, very likely that the variances are not the same.
The Levene's test perform an ANOVA test over the absolute deviations from each group's center.
The group center may be the mean or the median. When using the mean as group center the test is called the Levene's test, when using the medain as group center the test is called the brown forsythe test.
When performing ANOVA test, we try to determine if the difference between the MADs reflects a real difference between the groups, or is due to the random noise inside each group. The F statistic represents the ratio of the variance between the groups and the variance inside the groups. Unlike many other statistic tests, the smaller the F statistic the more likely the averages are equal.
Sample data from all compared groups.
k - number of groups.
ni - sample side of group i.
n - overall sample side, includes all the groups (Σni, i=1 to k).
x̄i - average of absolute differences from group's average, in group i.
x̄ - overall average (Σxi,j / n, i=1 to k, j=1 to ni).
Si - standard deviation of group i.
For the levene's, each value is the difference from the group's center.
|Source||Degrees of Freedom||Sum of Squares||Mean Square||F statistic||p-value|
|k - 1||MSG = SSG / (k - 1)||F = MSG / MSE||P(x > F)|
|n - k||MSE = SSE / (n - k)|
|Total||n - 1||SS(total) = SSG + SSE||Sample Variance = SS(total) / (n - 1)|