Homoscedasticity. Oops !! What's that ?

Homo = same; Scedastic = scatter (which we know by the name of 'variance' in statistics).
Before applying t-test, don't we find a term known as 'equality of variances' between the groups, which is done by the Levene's test. This is for testing homoscedasticity only. This is actually done by dividing variance of one group by variance of another group.
i.e.  .
If this ratio is much different from 1 (for which we always have table already generated by gr8 grandfathers of statistics), we say that the groups are not homoscedasctic.
One more application of this, we commonly find is that in calculating correlations in General Linear Model.
This is homoscedastic, as the scatter is uniform
This is non-homoscedastic (a.k.a. heteroscedastic), as the scatter is non-uniform.
In General Linear Models, to know the correlations, this is one of the assumptions to be met; the other assumptions being that the data should be normally distributed and there should be linearity present in the scatter. bye for now, folks...