Perhaps you are over-thinking this.
The straight-forward way to "control for multiple comparisons" would
be use a Bonferroni correction (or one of its variations) of the p-values
for the 5 separate t-test. Thus, your 5 initial 0.05 tests would be performed
at the 0.05/5 = 0.01 nominal alpha.
Or if you want an overall test, you would use one of the formulas for
What Levene's test indicates directly is a difference in variances,
not non-normality in itself. Why do you see it? If there is a
ceiling/basement effect, then there might be an underlying
transformation that would help; on the other hand, if that is
the problem, the original F-test is probably robust if the Ns are
reasonably equal and you don't have any *really* extreme
outliers. (I would not expect such extremes here, since this is
I do like to use a transformation to normalize scores, so long as
it comes naturally to the data. Since you are having trouble there,
I think you should be satisfied with the more basic solutions, suggested
Date: Sat, 25 Jun 2011 15:15:02 -0700
Subject: Question about non-normal data
I have depression scores (continuous variable) and a gender variable from five different countries (country variable: 1=chile, 2=cuba, 3=mexico, 4=argentina, 5=uruguay).
I wanted to find out whether there was a difference in depression scores based on gender, so I ran t-tests within each country.
I received a critique which stated that I had not controlled for multiple comparisons.
To address the critique I decided to run a univariate GLM, but my levene's test is significant and I have been trying to transform the depression scores but to no avail.
Does anyone have any advice on how to deal with a situation like this?
All suggestions are welcomed,