Is ratio of the maximum to the minimum of two normal sample variance a viable alternative to F-ratio test?

Abstract

Pandey and Bhattacharya (1986) derived the distribution of the ratio of the maximum to the minimum of two independent normal sample variances for testing the equality of their population variances. However, the usual test statistic is the F-ratio —the ratio of the two sample variances. In real applications of the F-ratio test, it is customary to use the larger sample variance in the numerator (McClave and Dietrich, II (1988), p. 460). In this short note, we show that if, instead of using the F-ratio test, one uses the ratio of the maximum to the minimum of two sample variances as a test statistic, the power of the test is very small questioning the viability of the test as an alternative to the F-ratio test.