Dear Anonymous 45858:

Calculating sample size for randomized controlled trials, either clustered or not, is more complicated than can be described here in a short EN-Net posting. Moreover, the implementation of randomized controlled trials is a complicated and detailed process which requires substantial expertise and experience. I would strongly recommend you find a competent statistician with relevant experience with whom to consult.

The information you provide in your posting is insufficient for sample size calculation. When you speak with your statistician consultant, you need to be able to provide, at minimum, the following information: 

1) You need to identify the outcome to be used to calculate the minimum sample size. Outcomes can be measured in dichotomous, categorical, or continuous measurements. The type of formula and the necessary assumptions to use for these different types of outcomes will be different, so you need to make these determinations beforehand. 

2) You need to determine what Is the minimum difference between study arms in the selected outcome you wish to detect with statistical  significance. If your selected outcome is expressed as a dichotomous variable, such as response to treatment versus no response to treatment, you will need to make an assumption regarding the proportion of control study subjects with the outcome value. If your selected outcome is expressed as a continuous variable, such as change in blood pressure measured in mm Hg, you will need to make an assumption regarding the standard deviation of your outcome.

3) You will also need to decide how you are going to measure the difference between study arms. You can look at the difference in the prevalence of the outcome, the relative risk between intervention and control study arms, or the percent change in the outcome.

4) I do not know why you stipulate the number of educational zones and schools in your initial posting. Is the educational zone a variable for stratified sampling? If so, then your statistician consultant will need to know this. Is the school the primary sampling unit defining the cluster? If so, the number of clusters you stipulate, 10, is probably far too few. Selecting only 10 primary sampling units will lead to a large cluster size which will result in a high design effect and substantial loss of precision. But determining the optimal cluster number and size is a complex topic to discuss with your statistician consultant.

I'm sorry to not be of much help, but, as mentioned above, it really is not possible to provide sufficient statistical advice on such a complex topic in this forum.

Kind regards,

Brad Woodruff

I read an article on the cluster randomized clinical trial. It is very interesting and highly scientific. Unfortunately, I cannot use the cluster randomized sampling calculation formula in a real life case.

Sample size calculations for a cluster randomised trial can be complicated. I think the sampel size issue for cluster sampled surveys is also somewhat overcomplicated eith guidelines usig obscure and conflicting terminology. Sample size formulae may give silly results (e.g. sample sizes larger than population sizes). I tend top tely on the algorithm present in:

Cochran WG, Sampling Techniques (3rg Ed.), Wiley, New York 1977

Which is clear and ell behaved. THis is covered in This  article:

Minassian Sampel Size for Eye Surveys

And i implement in the sampleXS  sample size calculator app..

I think the information you present:

    General population: 3,500,000 inhabitants

    number of educational zones: 5

    number of schools selected: 10 due to 2 per educational province

Is incomplete ... You will usually need to present (e.g.) expected proportions of success (or mean values) in control and intervention groups and a guess and thee at he intra-cluster correlation coefficient.

A decent text on this is"

Donner A ane Klatr N, Design and Analysis of Cluster Randomization Trials in Health Research, Arnold, London, 2000

You may find the "canonical" text:

Murry DM, Design and analysis of group-randomized trials, Oxford University Press, New York,1998

to be useful.

I agree with woody ... "the implementation of randomized controlled trials is a complicated and detailed process which requires substantial expertise and experience. I would strongly recommend you find a competent statistician with relevant experience with whom to consult". THe Murray (1998) reference cover (IMHO) most material you will need and is good fora avoiding the many pratfalls associated with clutter randomixed trials.

I hope this is of some help.