# Unequal sample size ANOVA

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### one-way ANOVA completely different sample numbers

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### one-way ANOVA completely different sample numbers

of focks »Tue 12 Jul 2011, 10:02 pm

Hello,
I am unfortunately an absolute beginner, so please answer a little "easier". Thank you very much.

The problem - (maybe it isn't):

I have 3 groups A, B, C who each received a different therapy after a laboratory value X was determined. However, this laboratory value does not have to have been the decisive point for the group classification (other factors also come into question).
The groups have completely different case numbers n A = 9, B = 16, C = 129.
When I do a one-way ANOVA, he tells me a highly significant H0 rebuttal.
Post-high analysis with Scheffe or Bonferroni shows me that A and B are the same, but A and B are highly significantly different from C.

SPSS notes that samples are not the same and therefore 1st order errors cannot be ruled out.
How can I now determine whether an ANOVA with my case numbers is permissible, or what would be more suitable?

Kruskal Wallis test is perhaps more robust in such small groups, but I can't do the posthoc analysis there.
Addendum ... the value X is not normally distributed.

Many Thanks
greeting
chris
focks
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### Re: one way ANOVA completely different samples

of PonderStibbons »Wed 13 Jul 2011, 7:30 am

Posthoch analysis with Scheffe or Bonferroni shows me that A and B are equal to one another,

The correct formulation is that the null hypothesis cannot be rejected in this comparison. A lack of evidence of inequality is not evidence of equality in the inferential statistics, especially in the case of very small case numbers.
SPSS notes that samples are not the same and therefore 1st order errors cannot be ruled out.

Can you post the precise wording? First-order errors can never be ruled out, so the wording tends to be nonsensical.

In particular, unequal samples can, under certain circumstances, increase the risk of an error, namely when the scattering of the groups is also very different. If the larger spreads occur in the cells with the smaller number of cases, the risk of type I errors increases. If the larger spreads occur in the cells with a larger n, on the other hand, the risk of type 2 errors increases.
How can I now determine whether an ANOVA with my case numbers is permissible, or what would be more suitable?

First take a look at the homogeneity of variance (Levene test).
Addendum ... the value X is not normally distributed.

Irrelevant. In an ANOVA, the output variables should not be "normally distributed" (come from a normally distributed population), but the prediction errors (residuals). And that is only of interest for smaller samples, but yours is already comparatively extensive.

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### Re: one way ANOVA completely different samples

of focks »Fri 15 Jul 2011, 7:25 pm

regarding the SPSS comment:
Means for groups in homogeneous subsets are displayed.
b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.
a. Uses Harmonic Mean Sample Size = 16,541.

The Scheffe test at SPSS shows me that as an additional grade.

According to the Levene test, my variable is not homogeneous within the group.

The problem with the residuals. I can display the residuals wonderfully, but I don't know how to test them for normal distribution.
Simply all as a new variable and KS test or is there a more elegant way?

The ANOVA with Posthoc would be nice and elegant if I could do it.
Plan B would be Kruskal Wallis test and then multiple testing with Mann Whitney TEst with an adjusted significance level p * 2 (Bonferoni correction).
Is that an option?

Thanks and regards
focks
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### Re: one way ANOVA completely different samples

of PonderStibbons »Sat Jul 16, 2011, 8:28 am

Simply all as a new variable and KS test or is there a more elegant way?

As already said, normal distribution is not an issue for the given sample size, but if you want to do it, then in fact via save / test.
Plan B would be Kruskal Wallis test and then multiple testing with Mann Whitney TEst with an adjusted significance level p * 2 (Bonferoni correction).

As far as I know, the ONEWAY procedure in SPSS has modifications for unequal variances (Brown-Forsythe and Welch) as well as a post-hoc test for unequal variances (Games-Howell). Bonferroni is by the way a correction of the type: new alpha = old alpha / number of tests, so here with 5% / 3.

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### Re: one way ANOVA completely different samples

of focks »Sat Jul 16, 2011, 1:57 pm

All right!

Thanks for the tips with the robust one-way.

Will it or have done it conservatively and of course with p / n.

Greetings and thanks so far.
focks
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### Re: one way ANOVA completely different samples

of idea »Tue 1st Nov 2011, 8:34 pm

I have a similar problem, maybe someone knows something about it:

4 conditions: 24, 33, 30, 23 subjects per condition. Levene test becomes significant. Now it is said, however, that the ANOVA is robust against violations of its prerequisites if the samples n> 10 and the and are of the same size (Bortz, 2005).

Can I assume random samples of the same size for myself? If so, could I also do the same with regard to gender (69 subjects female 38 male)?

It would be great if someone of you could help me!
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