Sample Size Estimation

Comparison of two means (dependent)

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Comparison of two means (dependent):
If your design has paired observations (e.g. before-and-after), then what seems to be a two-group test is really just a one-group test of whether the average change is different from zero. (See paired t-test in the Analysis II Module). Another description of this situation is that each subject is serving as his/her own control. In this case the sample size formula is:
N = (zα + zβ )2 / (δ/σ) 2
It looks very similar to the two-sample situation, but with two important changes. First, there is no multiplier of “2”. Second, the σ is the standard deviation of the differences within pairs, not the standard deviation of the original measurements. This is almost never known in advance, but as Streiner and Norman say, “On the brighter side, this leaves more room for optimistic forecasts.”

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