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Design effect in cluster sampling

The design effect is a correction factor that is used to adjust required sample size for cluster sampling. The required sample size is estimated assuming a random sample, and then multiplied by the design effect. This accounts for the loss of information inherent in the clustered design.

The design effect is a simple function of the average number of subjects sampled per cluster and of the intraclass correlation coefficient:

Algebraically speaking -

Design effect = 1 + (m-1) ICC

  • m is the average number of subjects sampled per cluster,
  • ICC is the intraclass (or intracluster) correlation coefficient

The larger the value of the intraclass correlation coefficient, the larger the design effect, and the more the sample size would have to be increased. If in extremis the ICC was equal to 1, one would have to treat each cluster as a single individual and multiply required sample size by the number of individuals per cluster.

Similarly the larger the cluster size, the larger will be the design effect. For small cluster sizes (< 5), the design effect may be very small, but for large cluster sizes the effect may be considerable, even with a small intraclass correlation coefficient.