n size reference

[Salbod]

Dear Friends,

                I am analyzing parenting measure with six subscales.  I want to examine the measure for differences of ethnicity using five groups: ns = 19, 21, 25, 3, & 2. I’ve done a series of one-way ANOVAs dropping group four (n=3) and five (n=2). The person I’m doing this analysis for wants groups four and five included in the analyses because they yield ‘interesting’ results. I’ve already explained the issue of n size, that their study, was under powered for medium and small effects.   What I am looking for is a rule of thumb reference for group n sizes in one-way ANOVA.

                Any light you can shed on this problem will be greatly appreciated.

 

Your friend,

 

Stephen Salbod, Pace University, NYC

 

[Martin Holt]

Dear Stephen,

Once you move away from just comparing two treatments, there is no longer one clear alternative hypothesis. You enter into the realm of multiple comparisons. To do an ANOVA is one approach, only doing pairwise comparisons after the global test is significant. The simplest way forward is to take a 3-way comparison, eg, as performing 3 independent trials, and to use conventional significance tests as per Saville (1990)*. The sample size to use is the maximum sample size from the three sample sizes over the three groups.

I've read that G*Power handles ss questions for ANOVA, and is free:
http://www.google.com/url?sa=D&q=http://www.psycho.uni-duesseldorf.de/aap/projects/gpower/&usg=AFQjCNG0yvUKvRSp-lpnFd19OaiITBpSFA

Naturally, you would want to review the assumptions being made, which I guess would include your question as to minimum n for each group.

The standard assumptions for ANOVA are:

Residuals are normally distributed. How to check when n=2, say?
Residuals have mean=0 and the variance of all the samples is equal.
Residuals are mutually independent. Look at the situation.
(The ANOVA test is known to be robust with respect to modest violations of the first two assumptions.)

 

Note there is no assumption stipulated over the minimum size of each group. Larger sample sizes give more reliable information and even small differences in means may be significant (in your ANOVA) if the sample sizes are large enough. As far as I know, the permissible value of n for each group is checked by the groups satisfying the above assumptions....I don't know of any rule of thumb...

 

Your ANOVA is wildly "unbalanced", however, and this takes you into a broad area theoretically. For example:

http://astro.temple.edu/~andykarp/psych522524/09_Advanced.pdf

 

Would there be any way of incorporating the two small groups into other groups ?

 

Finally, do you understand why these two groups are so different ? Are their sample sizes realistic ? If so, intuitively, I wonder if your research question is as focussed as it needs to be ?

*Saville , DJ (1990) Multiple comparison procedures: The practical solution. The American Statistician, 44, 174, -180

 

Best Wishes,

 

Martin Holt

 

----- Original Message -----
From: Salbod, Mr. Stephen
To: [hidden email]
Sent: Monday, January 18, 2010 4:18 PM
Subject: n size reference


Dear Friends,
                I am analyzing parenting measure with six subscales.  I want to examine the measure for differences of ethnicity using five groups: ns = 19, 21, 25, 3, & 2. I’ve done a series of one-way ANOVAs dropping group four (n=3) and five (n=2). The person I’m doing this analysis for wants groups four and five included in the analyses because they yield ‘interesting’ results. I’ve already explained the issue of n size, that their study, was under powered for medium and small effects.   What I am looking for is a rule of thumb reference for group n sizes in one-way ANOVA.
                Any light you can shed on this problem will be greatly appreciated.
 
Your friend,
 
Stephen Salbod, Pace University, NYC