SAMPLE SIZE REQUIREMENT TO SHOW THE EQUIVALENCE OF TWO TREATMENTS IN A PARALELL DESIGN

Abstract

The comparison of two treatments is often formulated on the basis of contrasting hypothesis of the form Ho: m1 = m2 against Ha: m1 ¹ m2 (null and alternative hipothesis respectively), where m1 and m2 are the population means of each treatment. This formulation of the problem is convenient when the aim is to demonstrate the truth of the alternative hypothesis, but it is not when the interest is to prove the equivalence of both treatments. For a bioequivalence study, Westlake (1988) developed a procedure to show the equivalence of two treatments for a crossover design. The aim of this paper is to adapt that procedure for parallel designs, including the sample size formula. The main advantage of this procedure is that it provides an explicit expression for the sample size for given values of a and b. Its disadvantages are that the real value of the significance level is strictly less than the nominal value of a, and that it requires that both samples come from normal distributions with equal variances.