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Henry Ford Hospital Medical Journal

Abstract

This paper introduces the use of the Weibull distribution function for the analysis of small samples of clinical data. It is compared with the use of the conventional analysis of variance in determining the results of a study comparing the use of gold salts and a placebo in the treatment of rheumatoid arthritis. Although the samples were small, 14 control patients and 13 who were treated, analysis of variance determined several significant differences between the two groups. The use of the Weibull distribution, however, not only confirmed these differences, but also determined several more differences between the two groups that were undetected by analysis of variance. A brief description and discussion of the Weibull distribution function is presented. It includes a method for determining the Weibull parameters, and the use of these parameters in identifying unknown samples as belonging to more well-known distribution functions such as the normal, exponential and Chi Square. A method for comparing two samples using an integration of the sum of the alpha and beta errors is also presented. Finally there is offered an explanation as to why the use of the Weibull distribution should be more sensitive in determining differences between small samples of data than more conventional methods of hypothesis testing.

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