Re: Datasets of unequal size and tiny variances

"Sean Richards" <somebody@xxxxxxxxxxx> writes:

> Hi,
>
> I have some generated datasets for which there is one factor 'a', which
> has 5 levels (the diffferent values of 'a' mean that the datasets are of
> different lengths). Some basic stats on the datasets:
>
> a Length Min Max Mean S.D. Var
>
> 1 100 -0.0030 0.0022 5.9591e-05 0.0010 1.0685e-06
> 10 1000 -0.0097 0.0102 0.0001 0.0036 1.2664e-05
> 100 10000 -0.0178 0.0187 -4.1100e-06 0.0051 2.6127e-05
> 1000 100000 -0.0276 0.0270 2.6589e-05 0.0061 3.7052e-05
> 10000 1000000 -0.0156 0.0159 4.2456e-06 0.0031 9.8627e-06
>
> The datasets are normally distributed.
> Some questions:

> My hypothesis is that the level of a has no effect.
> 1. So I can do a one way Anova to test this ?

Just following up on this. Results from the one way Anova are:


Analysis of Variance Table

Response: values
Df Sum Sq Mean Sq F value Pr(>F)
a 4 0.0001 1.440e-05 1.1558 0.3282
Residuals 1111095 13.8418 1.246e-05

If all assumptions for the one way Anova were met, I could conclude that
there were no significant differences. However the variances although
tiny show differences - ratio of largest/smallest = 35 (approx). How
robust is the Anova test with such a difference in variance, and if it
is a problem what do I do about it?

I also looked at the Kruskal-Wallis, test which depending on which reference
you use does/does not require equal variances. Which is true?

Cheers, Sean

--
"Hver sin smak", sa vintapperen, han drakk mens de andre sloss."
.

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