Effect size is a measure of the strength of the relationship between variables. Cohen's f statistic is one appropriate effect size index to use for a oneway analysis of variance (ANOVA). Cohen's f is a measure of a kind of standardized average effect in the population across all the levels of the independent variable.

Cohen's f can take on values between zero, when the population means are all equal, and an indefinitely large number as standard deviation of means increases relative to the average standard deviation within each group. Jacob Cohen has suggested that the values of 0.10, 0.25, and 0.40 represent small, medium, and large effect sizes, respectively.

Calculation

Cohen's f is calculated as

where σm is the standard deviation (SD) of population means (mi) represented by the ...