Dear Erik,

I am assuming that you have a sample of 17 observations and not 17 samples. It is hard for me to judge the equivalence of the variances without more information (e.g., the ranges of the data in the groups). The good news is that ANOVA has been shown to be quite robust to violations of the homogeneity of variance assumption except in certain instances. If the data a VERY highly skewed or bi-modal, violations could be problematic. I am not saying you can just ignore the Levene test, but with that small a sample, it is not too sensitive. I would suggest you run a Kruskal-Wallis in addition to the ANOVA as the K-W does not require that assumption. It the ANOVA and K-W results are similar, it is an indication that the violation of the homogeneity assumption did not impact your results.

Good luck,

J. McLean

Dear James E. McLean E. McLean,

Thanks for your answer! Although, I wasn't clear enough, you did answer my question I believe. But just to be sure. It is actually 17 samples, not 17 observations. I have a dataset on n = 11,000+ students across k = 17 schools (which make up the 17 samples). Across these 17 schools I want to compare the mean student satisfaction.

I wanted to avoid using the Kruskal-Wallis test because it will only tell me whether the variable school (with 17 categories) would only give me the significance. And with these kind of sample sizes it is unlikely the outcome would be insignificant.

Now, therefore I wanted to use a One-way ANOVA and compute the r-squared (i.e. explained variance).

But as you say, One-way ANOVA is rather robust against violations of homogeneity of variance. Distributions within the schools is rather consistent with a normal distribution, so I'm probably OK with using a One-way ANOVA.

Thanks!

Erik,

That is even better news! With that large a sample, the law of large numbers kicks in and you really should not have to worry much about that assumption. It would be analogous to a t-test versus a z-test for comparing two groups when the Central Limits Theorem kicks in.

Jim McLean

My data set contains 6 groups with 3 observations in each. I am trying to conduct a comparison of the means tests but I'm unsure which test to use. when I do a compare variance test amongst groups ( variance of the samples I am comparing are more than two to four times greater than one another, meaning variances are unequal). however, when I run Levene's test for variance it shows that my variances are equal.

I'm not sure which test to follow, the general rule or the levenes test. Please help?