6.5 Two

Two-way non-parametric ANOVA is an extension of the non-parametric one-way methods discussed previously. The basic procedure is to rank all the data in the sample from smallest to largest, then carry out a 2-way ANOVA on the ranks. This can be done either for replicated or unreplicated data.

Using the data file Stu2wdat.csv , do a two-factor ANOVA to examine the effects of sex and location on rank(rdwght).

To calculate the Scheirer-Ray-Hare extension to the Kruskall-Wallis test, you must first calculate the total mean square (MS), i.e. the variance of the ranked data. In this case, there are 186 observations, their ranks are therefore the series 1, 2, 3, …, 186. The variance can be calculated simply as var(1:186) (Isn’t R neat? Cryptic maybe, but neat). So we can compute the H statistic for each term: