>Hi
>
>DG> Deborah, I'll be interested to see responses from others, as
>DG> I don't think there will be an ironclad truism, but here is my
>DG> two-pence
>
>Here's mine.
>
>DG> (1) even though often we hear that ANOVA is "robust" to
>DG> moderate violations of the assumptions, there are some papers that
>DG> show this is not necessarily the case when sample size markedly
>DG> varies across groups (e.g., if the larger variance is associated
>DG> with the larger group tests of signficance tend to be
>DG> conservative); so, to the extent that your design is relatively
>DG> balanced, that will be of less concern that if it is not.
>
>Normality is in general considered less important than homogeneity of
>variances. As you point out, unbalanced designs are more affected by
>lack of HOV. I read (but I don't have the reference here right now)
>that lack of HOV will severely affect the ANOVA p-value if the
>smallest sample is lower than 10 cases and the biggest sample is more
>than four times the smallest. If the biggest samples has the smallest
>variances, true significance level increases, and if biggest samples
>have biggest variances, true significance level disminishes (I hope my
>explanation is clear, even in Spanish it was a bit difficult to
>understand, and the translation hasn't improved it).
>
>For Oneway ANOVA, SPSS incorporated (since version 9, I believe)
>robust tests: Brown-Forsythe and Welch (this last is more adecuated
>for heavily unbalanced designs).
>
>Even if lack of HOV doesn't have much impact on the overall p-value
>(in balanced or moderately unbalanced designs), it can have a lot of
>effect on multiple comparison methods. Replace Tukey..., or any
>post-hoc method you use, by Tamhane test. Also, contrasts (orthogonal
>or not) are adjusted for lack of HOV (I'm talking about SPSS'
>procedure ONEWAY).
>
>DG> (2) Though there are myriad opinions about transformations
>DG> (e.g., log, reciprocal, etc.), if the normality assumption is not
>DG> tenable, attempt a transformation (one ideally that can be
>DG> justified) and see if your general results/conclusion holds
>
>As I mentioned before, ANOVA is quite robust to departures of
>normality (as a matter of fact, Levene test is an ANOVA with the
>absolute values of the residuals, which have a highly skewed
>distribution). Besides, transformations that fix lack of HOV usually
>improve normality, therefore I recommend you to focus on those
>transformations that stabilize variances and see the effect on
>normality.
>
>A list of the most popular transformations:
>
>- If SD is proportional to the mean, then a log transformation will
>improve both HOV & normality (distributions tipically log-normal,
>positively skewed). This transformation has the advantage of being
>"reversable": you can back transform the data and obtain geometric
>means or ratio of geometric means (when you back transform logmean
>differences). Use x'=(log(1+x) if there are zeroes (problems back
>transforming data can arise in this particular case).
>
>- If variance is proportional to the mean, then you have distributions
>that follow Poisson distributions (or overdispersed Poisson
>distributions: Negative binomial) and square root can help. Again, add
>1 before taking the square root if zeroes are present. This
>transformation can't be back transformed for mean differences.
>
>- For binomial proportions with constant denominators, you can use the
>angular transformation: x'=arcsin(sqrt(p)). Again, it can't be back
>transformed for mean differences.
>
>- Reciprocal transformation: x'=1/x. I can't remember right now when
>it was indicated.
>
>See:
http://bmj.bmjjournals.com/cgi/content/full/312/7039/1153 for an
>interesting Statistics Note on the problems of back transforming CI
>for mean differences.
>
>Also, this note
>
http://bmj.bmjjournals.com/cgi/content/full/312/7038/1079 focuses on
>the problem of trying to back transform the SD after a log transform.
>
>DG> (3) You can always resort to a nonparametric analogue
>DG> (e.g., Kruskal-Wallis) and again check if the general results
>DG> obtained...
>
>This could be OK if the only problem is lack of normality, but if you
>also have lack of HOV you should not use Kruskal-Wallis test. Citing a
>previous message of mine (from the Tutorial on non-parametrics series
>I started in April):
>
>"Data requirements for Kruskal-Wallis test: distributions similar in
>shape (this means that dispersion is something to be considered too;
>see: "Statistical Significance Levels of Nonparametric Tests Biased by
>Heterogeneous Variances of Treatment Groups" Journal of General
>Psychology, Oct, 2000 by Donald W. Zimmerman. Available at:
>
http://www.findarticles.com/p/articles/mi_m2405/is_4_127/ai_68025177 )"
>
>HTH,
>
>Marta
>
>
>
>