Certain sample size needed for HLM?


New Member
I have a data set of test scores and memory scores of 111 students, nested in 12 different classroom. 6 classrooms are from high income areas and 6 from low income areas. The number of students in each classroom ranges from 2 and 12.

I am looking to see if the effect of income area on test scores is mediated by memory capacity.

Is this sample size of 111 too small to use for HLM?

I want to control for the fact that the students are nested in classrooms, but think my sample may be too small?

A post on HLM power and sample size has been discussed elsewhere. You may want to see it here: http://www.talkstats.com/showthread.php?t=9366 for some preliminary thoughts.

As an add-on, although it would be interesting to see the effects you speak of, I don't think you have sufficient people in the sample to run an HLM model. My general understanding is that you need 25 people per group (and about 25 groups) to have sufficient power to your analysis.

Hope this helps.


TS Contributor
It is true that you usually require large samples for this kind of models, but a small sample should not stop you from using it, if the assumptions are met.

I'm really not a huge fan of those "rules of thumb" and I'd like to add that I'm aware of studies with a sample size of around 100 where HLM has been used. This is specially common for Longitudinal data, where you usually can't afford too many subjects in your study. Just as an example, a common popular database, the Mini Wright data, involves only 17 subjects. I really didn't like the "sampling" used in this study, but it is still a good application for HLM that didn't have many subjects available.

So, I don't think sample size should be an impediment for developing the analysis, even if the power is low.
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I tend to agree that rules of thumb are not always ideal and should not necessarily be followed to the letter. As a matter of fact, I also see HLM designs that have 100 people or so. I think the point made is right - if you meet the assumptions with your sample, then it can be justified. However, estimating slopes of groups using 2 people may be problematic in this particular instance. I had to renounce doing HLM in my current study do to a similar problem. Without any empirical support, my general thoughts are that 10 people per group would be a nice minimum to achieve, but then again, I guess it is very sample specific.