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Table 1 Effect size and sample size formulae

From: Sample size and power estimation for studies with health related quality of life outcomes: a comparison of four methods using the SF-36

  Method 1 Method 2 Method 3
Assumptions Normally distributed continuous data Non-normally distributed continuous data Ordinal data, constant and relatively small odds ratio, large sample size
Summary Measure Mean and mean difference Median Odds Ratio (OR Ordinal )
Hypothesis test Two-independent samples t-test Mann-Whitney U test Mann-Whitney U test or equivalent proportional odds model
Effect Size p Noether = Pr(Y >X)
Sample size formulae
  1. Δ Normal is the standardised effect size index, μ T and μ C are the expected group means of outcome variable under the null and alternative hypotheses and σ is the standard deviation of outcome variable (assumed the same under the null and alternative hypotheses). pNoether is an estimate of the probability that an observation drawn at random from population Y would exceed an observation drawn at random from population X. Let π iT be the probability of being in category i in Group T and γ iT be the expected cumulative probability of being in category i or less in Group T (i.e. γ iT = Pr(Y ≤ yi)). is the combined mean (of the proportion of patients expected in groups T and C) for each category i. z1-α/2and z1-β are the appropriate values from the standard Normal distribution for the 100 (1 - α/2) and 100 (1 - β) percentiles respectively. Number of subjects per group n for a two-sided significance level α and power 1 - β.