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I am currently analyzing the results of my study which deals with several dependent variables. I have tested the data for normality and homogeneity and all but one passed the assumptions for ANOVA. This particular variable passed Shapiro-Wilk test but failed Levene's test. The homogeneity is not just a minor violation but a significant one since the p-value is 0.000. My question is can I use Kruskal-Wallis test to analyze this one particular variable while using ANOVA for the others. Will that be acceptable?

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If your data passes normality tests, but fails test for homogeneity of variances, you can use Welch's ANOVA (and Games-Howell test as a post-hoc for pair-wise comparisons).

An example how to do the tests in R:

data(Moore, package = "car")

# Welch's ANOVA
oneway.test(fscore ~ fcategory, data = Moore)

# Games-Howell test
library(userfriendlyscience) 
posthocTGH(Moore$fscore, Moore$fcategory, method = "Games-Howell")

You can read more about Welch's ANOVA here, here and here.

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Yes, it is acceptable. It depends though on your sample size (if very large then you could have violations of normality assumptions which are not crucial, and the central limit theorem also applies). In addition, it depends on what the prior literature has told you regardin this variable.

In any case, if you are not doing complex analysis, then Kruskal-Wallis test has a power smaller than ANOVA but still quite substantial (possibly better still than ANOVA when the distribution is skewed, as reported by Van Hecke).

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  • $\begingroup$ Thank you for the answer, Giuseppe. Yeah, the distribution is not only slightly skewed but has several peaks. I guess I will be using Kruska-Wallis. I just hope the data passes non-parameteric homogeneity test this time. If not, I don't know what to do then. $\endgroup$ – P. Jim Mar 24 '16 at 8:20
  • $\begingroup$ Kruskal-Wallis is quite robust and loss of power is not that big even if the distribution is symmetrical. Remember that if you want to be even more robust you can always use bootstrap. $\endgroup$ – Joe_74 Mar 24 '16 at 8:56

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