help with unequal variances

Hello,

I have some patient data for my masters thesis with three groups (n=16, 19
& 20)

I have completed compiling the results of 7 tests, for which one of these
tests the variances are unequal.


I wish to perform an ANOVA between the three groups but for the one test
with unequal variance (<0.001 by both bartlett and levene's test) I am not
sure what to do.

I thought i would run ANOVA with bonferonni post-test for groups with
equal variances, then for the test with unequal variance i would use the
welch correction and games-howell post-test.  Does this sound reasonable?

Someone has also recommended to me to use Kruskal-wallis ANOVA, then use
Wilcoxon sign rank test pairwise to determine which groups are
significantly different (ON ALL DATA, both equal and unequal variance
tests).  I don't think this is right, for two reasons:

1) Kruskal-wallis is for non-gaussian data, and i have no reason to
believe they are not normal.
    - I have run normality tests which say they are normal, although
perhaps my sample sizes are too small for a normality test?
2) i believe running pairwise Wilcoxon sign rank test is not acceptable
unless there is a post-test correction for multiple comparisons (i am not
aware of one); also on the wiki page for this test one of the assumptions
says "Under the null hypothesis the distributions of both groups are
equal" which i read to say that the variances must be equal.

So I think there recommendations were based more on sample size and
normality, and not my issue with variance?


Ultimately i would like to know if i am going about this right with my
deduction (ANOVA/Bonferonni of the test results, but welch correction and
games-howell for the test with significantly different variances).  and if
not why and/or what you think is a better option.

most appreciated to any help received!