Mann-Whitney U Test or One-way ANOVA - Welch F test?

[klm]

I have two groups (Site 1 and Site 2) and would like to look at differences between the sites. The data violates assumptions of homogeneity of variance and the sample sizes are different. However, I have read that the Welch F statistic or Brown & Forsythe F-ratio are robust in this case. In the Mann-Whitney test my U value is huge (38313.00). In both tests P<0.001

Also when I look at 3 sites I have the same problems with assumptions of homogeneity although sample sizes are the same (different data). Is it better to use Anova with Games-Howell post hoc or Kruskal-Wallis with Mann-Whitney post hoc (using bonferroni probabilities)?

I am very confused as to how robust these tests are to violations of assumptions.

Thank you in advance for your help on this!

[Karabiner]

Robustness to a large part depends on the sample size.

Regards

K.

[klm]

In the test between 2 sites, the sample sizes are: site 1 = 528 and site 2 = 220. So they are quite different. Is it better to transform the data and see if it still violates assumptions?

[Karabiner]

What are the standard deviations (and the means, by the way)? I wonder whether
with a sample as large as yours you really have to doubt whether your result is
reliable. Anyway, the Welch t-test would be a good choice.

Regards

K.

[klm]

Hello again
They are are Site 1: Mean 4.18 SD 2.25 and Site 2: Mean 2.94 SD1.53
Thanks for your help on this.

[Karabiner]

As mentioned above, the Welch test is a good choice here. But for sake of
completeness: since your smaller subsample has the lower SD of both groups
the t-test is more conservative (i.e. produces fewer type 1 errors if H0 is actually
true) than it would be with equal SDs. That means, if you reject the Null hypotesis
than it's not due to making a mistake because of violation of assumptions.

Regards

K.

[klm]

Thanks Karabiner. You have been a great help!