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In the following Paper by Clare Rutterford, Andrew Copas and Sandra Eldridge, the following formula is given for sample size calculation:

Formula

assuming the following properties:

• m - number of clusters

• n - size of each cluster

• $\alpha$ - significance level for the two sided test

• 1-$\beta$ - power

• $\sigma^{2}$ -common variance for the two groups

• $\rho$ -The intra-cluster correlation coefficient

I tried to reach the same formula by myself but have not succeeded. If someone have the original computation it will be very helpful as well.

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    $\begingroup$ Does the Wikipedia article on design effect help you? $\endgroup$ – mdewey Jan 3 '17 at 13:31
  • $\begingroup$ not really because I don't understand what is the DE and how to proceed with it $\endgroup$ – Lambda87 Jan 4 '17 at 8:22
  • $\begingroup$ When you ask about the "original computation" are you asking the derivation of the formula you've just shown, or are you asking us to provide an example of this formula being applied in a specific situation? $\endgroup$ – user140401 Jan 4 '17 at 9:11
  • $\begingroup$ I am asking for the derivation of the formula $\endgroup$ – Lambda87 Jan 5 '17 at 10:54

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