Re: F-test: Varying standard deviations for populations in a 2 way ANOVA

On May 10, 3:57 pm, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
AndreHaupt wrote:
Good day,

I'm doing a 2 way ANOVA (2 x 7) to determine whether a certain row and
column combinations provide significantly better results. (Each
combination being a percentage between 0-1.)

The data in csv format:http://ahaupt.googlepages.com/data.csv(20
observations per cell).

Thus, there are 14 populations. Normality probability plots show that
the populations are normally distributed. I get the following standard
deviation values for each:
0.1448 0.1476 0.0753 0.1408 0.1499 0.1058 0.1410
0.1546 0.1477 0.0684 0.1346 0.1569 0.1112 0.1435

According tohttp://en.wikipedia.org/wiki/F-test, the F-test assumes
similar standard deviations for each population. This is clearly not
the case in my situation, even though the majority are around
0.14-0.15.

How would this affect my ANOVA results? (http://ahaupt.googlepages.com/
anova2.csv)

Your thoughts would be much appreciated.

Regards,
Andre

ANOVA is quite robust to departures from homogeneity of variance,
especially when all sample sizes are equal. One commonly used rule of
thumb (for the equal sample sizes case) is that if the largest variance
is not more than 4-5 times greater than the smallest variance, the
F-test should be pretty good.

--
Bruce Weaver
bwea...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx/wv/bwhomedir

Thanks for the advise. It seems to be the case with the largest
variance being 5.2637 times greater than the smallest.

.

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