When divided by the degrees of freedom (i.e., based on the number of subjects per group), the denominator of the F ratio is obtained.
Under the truth of the null hypothesis, the sampling distribution of the F ratio depends on the degrees of freedom for the numerator and the denominator.
This rank-based procedure has been recommended as being robust to non-normal errors, resistant to outliers, and highly efficient for many distributions.
For example, Monte Carlo studies have shown that the rank transformation in the two independent samples t-test layout can be successfully extended to the one-way independent samples ANOVA, as well as the two independent samples multivariate Hotelling's T2 layouts[2] Commercial statistical software packages (e.g., SAS) followed with recommendations to data analysts to run their data sets through a ranking procedure (e.g., PROC RANK) prior to conducting standard analyses using parametric procedures.
As the number of effects (i.e., main, interaction) become non-null, and as the magnitude of the non-null effects increase, there is an increase in Type I error, resulting in a complete failure of the statistic with as high as a 100% probability of making a false positive decision.
[citation needed] In general, rank based statistics become nonrobust with respect to Type I errors for departures from homoscedasticity even more quickly than parametric counterparts that share the same assumption.
"[18] According to Hettmansperger and McKean,[19] "Sawilowsky (1990)[20] provides an excellent review of nonparametric approaches to testing for interaction" in ANOVA.