pANOVA hypotheses:
pData should come from independent random samples, all Normally distributed with the same standard deviation
pKruskal-Wallis hypotheses:
p1.  Data should come from independent random samples, the response has a continuous (but not necessarily Normal) distribution.
p
p
p2.  Data should come from independent random samples, the response has a continuous (but not necessarily Normal) distribution, and the samples come from population distributions of the same shape (not necessarily Normal).
Comparing several samples:  the Kruskal-Wallis test