On cochran's and hartley's tests for homogeneity of variances when observations are autocorrelated

Abstract

An approximation to the p-values of the standard Cochran's and Hartley's tests for testing the homogeneity of variances is obtained for the case when the observations are autocorrelated. More specifically, the expression for calculating the p-value of Cochran's test for k(≥2) populations is given in terms of a multiple integral, whereas a series form is presented for the case of Hartley'stest. As, in practice, the tests for homogeneity of variances for 2 or 3 populations are often encountered, the closed form expressions for the p-values of these two cases are provided. For Cochran's test, we also provide suitable upper and lower bounds of the p-value for the general case of kpopulations. Numerical discussions are also given.

Keywords:

• Correlated data
• gamma approximation
• effect of autocor-relations on dispersion test
• pvalues
• upper and lower bounds