This paper discusses power and efficiency properties of the model proposed by Longini and Koopman for quantifying and testing secondary attack rates gathered from final size distribution data on infections in households. Sample size requirements are offered for a generalized likelihood ratio test that makes use of the secondary attack rate parameter implicated in the Longini-Koopman model. The appropriateness of this statistic is also considered. In addition, a sequential likelihood ratio test of a secondary attack rate parameter is derived for infectious diseases with short latency or asymptomatic periods. A comparison of the proposed sequential and fixed sample tests is described. Finally, applications involving final size distributions of household influenza infections are used to illustrate the practical merits of the proposed tests.