A Computing the Required Sample Size

  1. Identify your design estimate – this is the estimate that will underlie a headline you could imagine being written about your survey.

  2. Identify the desired MOE, \(m\), for this design estimate, noting whether you want this MOE to apply to the overall estimate, or for that estimate in each of, say, \(H\) subgroups/strata.

  3. Compute the sample size required, \(n_1\), assuming that you’re going to select a Simple Random Sample and ignoring the fpc.

    For estimation of a mean \(\bar{Y}\) of some characteristic \(y\): \[ n_1 = \left(\frac{Z}{MOE}\right)^2 s^2 \] where \(Z\) is appropriate for the desired level of confidence and \(s\) is the estimated population standard deviation of the characteristic \(y\).

    For estimation of a proportion \(P\): \[ n_1 = \left(\frac{Z}{MOE}\right)^2 p(1-p) \] where \(p\) is the estimated proportion, or 0.5 if really unknown.

  4. If the sample size is a substantial proportion of the population or subgroup size \(N\), then apply the fpc adjustment: \[ n_2 = \frac{n_1}{1+\frac{n_1}{N}} \]

  5. If you have \(H\) subgroups and are using equal allocation then multiply by \(H\) \[ n_3 = Hn_2 \] or alternatively sum over the \(n_2\) values in each of the strata you’ve defined.

  6. Apply the design effect (Deff) appropriate for the actual design you’ll be using. \[ n_4 = \text{Deff}\times n_3 \]

  7. Adjust for anticipated non-response: if response rate \(\phi\) is expected then \[ n_5 = \frac{n_4}{\phi} \] (If non-response is likely to vary between strata, then apply this correction to \(n_2\), within each stratum.)