An asymptotic test for the equality of coefficients of variation from k populations

Abstract

The coefficient of variation is often used as a guide of the repeatability of measurements in clinical trials and other medical work. When possible, one makes repeated measurements on a set of individuals to calculate the relative variability of the test with the understanding that a reliable clinical test should give similar results when repeated on the same patient. There are times, however, when repeated measurements on the same patient are not possible. Under these circumstances, to combine results from different clinical trials or test sites, it is necessary to compare the coefficients of variation of several clinical trials. Using the work of Miller, we develop a general statistic for testing the hypothesis that the coefficients of variation are the same for k populations, with unequal sample sizes. This statistic is invariant under the choice of the order of the populations, and is asymptotically chi 2. We provide an example using data from Yang and HayGlass. We compare the size and the power of the test to that of Bennett, Doornbos and Dijkstra and a statistic based on Hedges and Olkin.