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confidence intervals, effect size, parameter estimation, power, sample size, smallest benefit of clinical importance



  1. Corty, Eric W.
  2. Corty, Robert W.


Background: Sample sizes set on the basis of desired power and expected effect size are often too small to yield a confidence interval narrow enough to provide a precise estimate of a population value.


Approach: Formulae are presented to achieve a confidence interval of desired width for four common statistical tests: finding the population value of a correlation coefficient (Pearson r), the mean difference between two populations (independent- and dependent-samples t tests), and the difference between proportions for two populations (chi-square for contingency tables).


Discussion: Use of the formulae is discussed in the context of the two goals of research: (a) determining whether an effect exists and (b) determining how large the effect is. In addition, calculating the sample size needed to find a confidence interval that captures the smallest benefit of clinical importance is addressed.