The Matched Pairs Design in the Case of All-or-None Responses

The properties of the matched pairs design in the case of all-or-none responses have been the object of an increasing research interest. Wald (1947 p. 108) pointed out that pairing on the basis of some irrelevant criterion leads to a loss of efficiency in small samples. This matter was later scrutinized by Youkeles 19631 who concluded that the loss vanishes as the sizes of the comparison series become 30 or more. A condition on which matching produces a gain in efficiency was derived by Worcester [1964. Empirical work on the efficiency of the design was conducted by Billewicz 1964, 1965. M 1966 derived asymptotic results for power, sample size, and efficiency, but the nature of the approach limnits the applicability of the results to the vicinity of the null state. In the present work, general asymptotic results for power, sample size, and efficiency are derived for fixed sample size procedures inl the case of all-or-none responses. Application to an epidemiologic problem is shown.