# Nonparametric alternative to ANOVA for testing the difference between several brand preferences

I have collected a data from about 200 customers on their brand preference of 5 international fast food chain shops. Each customer was asked to rank all the 5 brands from highest to lowest (5 for the most preferred and 1 for the least preferred brand). The brand rankings will vary from one person to another.

I want to test if there are significant differences between the brand preferences.

At a fist glance ANOVA seems to be a good option. We could take the average of the ranks for each brand and then perform ANOVA. But the problem is that, the ranks can not be treated as scale, because the spaces among the ranks may not be equal. (e.g. Brand-2 and Brand-3 may differ a lot to a customer according to his preference than Brand-1 and Brand-2).

So, what can be the best alternative to test if the brand preferences are significantly different? I think I should adopt some non-parametric test like test of several medians instead of mean. What would be your suggestion regarding that? Will Kruskal-Wallis be a valid test here?

Would you please give me some indications as to how I should perform whatever you suggest in either R or in SPSS?

The answer is Friedman test. It is nonparametric and as you can see on Wikipedia, there is also very similar example as yours ("n wine judges each rate k different wines. Are any wines ranked consistently higher or lower than the others?").

See R package pgirmess and friedman.test() function that takes datamatrix as input. Note that if your null hypothesis is rejected, friedmanmc() function does post hoc analysis.

Kruskal-Wallis test is not appropriate in case of repeated measures.

• +1 for Friedman test, I use it often with the Nemenyi post-hoc test and plot it as critical distance diagram. (I have an R script for this, I'm searching for it right now) Commented Oct 10, 2012 at 9:31

There are two solutions much better than Friedman.

1. ART (Aligned-Rank Transform) ANOVA with Error term specified
2. Wald-Type Statistics

Both allow for more than one categorical covariate and interactions between them.