# Unequal sample size ANOVA

## STATISTIK-FORUM.de

### one-way ANOVA completely different sample numbers

All about (M) ANOVA, ALM ...

6 posts • Page

**1**of**1**### 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

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**- Greenhorn
**Posts:**9**Registered:**Sun 10 Jul 2011, 6:52 pm**Thank you given:**3**Thank you get:**0 times in 0 post

### 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.

greeting

P.

---

Thank god ... canon for 36

**PonderStibbons**- Forum supporters
**Posts:**9527**Registered:**Sa 4th Jun 2011, 2:04 pm**Place of residence:**Ruhr area**Thank you given:**36**Thank you get:**2009 times in 1996 posts

**the following users would like to thank PonderStibbons:**

focks

### Re: one way ANOVA completely different samples

of **focks** »Fri 15 Jul 2011, 7:25 pm

Thanks for the answer.

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

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**- Greenhorn
**Posts:**9**Registered:**Sun 10 Jul 2011, 6:52 pm**Thank you given:**3**Thank you get:**0 times in 0 post

### 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.

greeting

P.

---

Thank god ... canon for 36

**PonderStibbons**- Forum supporters
**Posts:**9527**Registered:**Sa 4th Jun 2011, 2:04 pm**Place of residence:**Ruhr area**Thank you given:**36**Thank you get:**2009 times in 1996 posts

**the following users would like to thank PonderStibbons:**

focks

### 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.

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**- Greenhorn
**Posts:**9**Registered:**Sun 10 Jul 2011, 6:52 pm**Thank you given:**3**Thank you get:**0 times in 0 post

### 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!

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!

**idea**- Greenhorn
**Posts:**9**Registered:**Fri Sep 16, 2011 10:18 am**Thank you given:**2**Thank you get:**0 times in 0 post

6 posts • Page

**1**of**1**Back to analysis of variance

### Who's Online?

Users browsing this forum: Bing [Bot], Google [Bot] and 0 guests

Powered by phpBB

Supported by

Supported by

- Do men really want monogamy
- How do marketing professionals do research
- How do free iOS apps make money
- Why is finance a good major
- Widespread access to wireheading would destroy society
- How does Danish differ from other languages?
- Killing dating apps long term relationships
- How do I become an agricultural engineer
- Cycling reduces bottom fat

- Why do we unconsciously make mistakes
- How is PDM University doing
- Why is yoga so popular with foreigners
- When is the data set not distributed normally?
- Are waist trainers dangerous
- What is the secret behind India's booming economy
- Should we really trust telepathic communication
- IBS is a great choice
- How can a teenager write for money
- Why did Amazon start Amazon Echo
- What did you recently present to your mother
- Which actor would be the best joker
- What was the name of Pavlov's dog
- Why is MMA considered safer than boxing
- What would an antimatter explosion look like
- Who were the people who became knights
- A fertilizer is an inorganic salt
- Who is Tillakaratne Dilshan 1
- What's wrong with this picture 4
- Support QuickBooks the latest GST billing
- Planets have their own light
- She sent this to me. What does that mean
- Is it possible to do telekinesis?
- What is Invisimol malware