Compute anova effect size from F-statistic
This might be combined with convert_effectsize_fsqu
This instance contains effect size measures f2, eta2, omega2 and eps2 as attributes.
This uses the following definitions:
f2 = f_stat * df1 / df2
eta2 = f2 / (f2 + 1)
omega2 = (f2 - df1 / df2) / (f2 + 2)
eps2 = (f2 - df1 / df2) / (f2 + 1)
This differs from effect size measures in other function which define
f2 = f_stat * df1 / nobsor an equivalent expression for power computation. The noncentrality index for the hypothesis test is in those cases given by
nc = f_stat * df1.
Currently omega2 and eps2 are computed in two different ways. Those values agree for regular cases but can show different behavior in corner cases (e.g. zero division).