Failure of Levene's test for equality of variance

[dune2]

Hey all, I am currently working on the statistics part of my Master thesis and I am conducting an ANOVA test to compare mean variances between three samples. Four out of the 15 compared variables do not satisfy Levene's test for equality of variance.
I know that ANOVA is relatively robust and most likely still offers valid results. Nonetheless, I will need to test the four variables for if they are truly different and I will have to choose and explain if and why ANOVA results are nonetheless valid.
How "safe" is ANOVA with these limitations and what test can I run (I am using SPSS 13 XP) to clarify the situation? Thanks a bunch!

 

[EnumaElish]

ANOVA is a test between means which makes use of the sample variances. You said you are testing whether the variances are equal across the samples, using Levene's test. Have you tried the alternative Bartlett test? In particular,

If you have strong evidence that your data do in fact come from a normal, or nearly normal, distribution, then Bartlett's test has better performance.

You may try to transform the data (e.g. take logs) and hope that this solves the problem. See http://www.unf.edu/~dmohr/sta5126/chap6.pdf#search='levene%20test']this[/PLAIN] pdf file.

 

[EnumaElish]

Also bear in mind that One-factor anova is "a generalization of the two-sample t-test." The 2-sample t-test can deal with unequal variances, which leads me to think that so can ANOVA.

The variances of the two samples may be assumed to be equal or unequal. Equal variances yields somewhat simpler formulas, although with computers this is no longer a significant issue.

But, a particular software package may not have this option. In some ANOVA packages (like SAS) specifying the "Welch" option controls for unequal variances.

 

[dune2]

Thanks for the answers. I'm still wondering thought, if I use the Welch Option in SPSS ) I can tick a box and then I get another printout for that), will I be on the safe side to use the finings, or do I have to discard/be more cautious with the results that indicate unequal variaance?

 

[EnumaElish]

As long as you are using the Welch option, you can say "while I realize that the variances may be unequal across samples with some probability, I am compensating for this by using the best [the only?] tool available in SPSS."

Other than this, you can either try transforming your sample or switch to using nonparametric tests.

 

[dune2]

Other than this, you can either try transforming your sample or switch to using nonparametric tests.

You mean like using logs, right? I am contemplating that right now for another part of my study (regression) but it becomes such a pain to infere the correct results from logarithmic results. Urgh!
Ah well, I guess I'll just stick to your defence for the ANOVA answers and if I actually have to recalculate all my data to logs, I can still ru the set again and see if the results differ!

 

[EnumaElish]

Why don't you use regression instead of ANOVA? See this http://www.epa.gov/bioindicators/primer/tableall.html ; it explains how you can code your variables to use regression instead of ANOVA.

 

[mimosa]

i did the two way anova.
but the variances were not equal.
i had transformed the data but still get the unequal variances.
should i compared the each groups but using the Post hoc test?

 

[statdad]

Classical ANOVA is not truly robust with respect to unequal variances - converting the problem to a regression model is really going in circles, as the underlying notions and many calculations are the same.

Have you graphed the data - how symmetric or non-symmetric are the samples? You can try transformations all week, but at some point the you will waste more time than is practical. Have you (or your advisor) thought/discussed an analysis based on R-estimates, or some other robust approach? I have a feeling that may be your best bet.

 

[mimosa]

i transformed the data but the result still the same.
someone suggested me analyze separately...
will get the advise from the advisor
hopefully can solve this problems

cheers