# Calculating needed sample size for two stage stratified cluster sample

We want to carry out a survey to assess perceptions of quality and access to medical education of last year students. Based on our research, we have decided that a two stage stratified cluster sample suits our needs in terms of costs and logistics. We have 37 medical institutions in the country so the first stage will be stratified and will have 4 strata:

• Strata 1 - Public and Urban
• Strata 2 - Public and Rural
• Strata 3 - Private and Urban
• Strata 4 - Private and Rural

The institutions in each strata will be selected randomly with the number of institutions to be selected from each stratum proportional to the total stratum size. For the second stage we will randomly select a number of students from registry lists.

How do you calculate the needed sample size (number of PSUs and SSUs)? (I am using Stata.)

• Welcome to the site, @Sante. I would probably go with all institutions, unless it is very expensive to add another university, as otherwise you'll end up with too few degrees of freedom; and stratify within institutions. Generally, the sample size is determined from either your budget (in which case, the sample size is but a moot point), or from your precision requirements (e.g., you want to have the percentage estimates to be within 1% of the target, or for your estimates of the total have CV < 0.1). I talked about sample size and power in surveys in dx.doi.org/10.1002/9781118594629.ch29 – StasK Apr 21 '15 at 15:53
• @Sante to answer this question we would need some information about the analysis you would like to do, the effects you would want to detect, the type I risk you want to control for and the power with which to detect the effect. Alternatively, we need the desired precision of the confidence intervals. – Momo Apr 21 '15 at 16:07
• @StasK is right. In general, it is better for you to have more clusters with relatively fewer students in each cluster than fewer clusters with more students per cluster, especially if you suspect intracluster correlation to be high (probably applies in your problem). As a trivial example, if your budget only allows for 200 students to be interviewed, it is better for you to have 20 clusters with 10 students/cluster than 5 clusters with 40 students in each cluster. – Marquis de Carabas Apr 21 '15 at 17:25
• See my answer to a similar question at: stats.stackexchange.com/questions/122274/… I would only add to that answer a reference to Kish (1965), p. 268 "Specific Cost Function for Cluster Samples". – Steve Samuels Apr 28 '15 at 12:40