On using hartley's statistic to test the hypothesis of not much difference among normal variances

In this paper we investigate the significance level and power of the Hartley's maximum F-ratio test for testing the null hypothesis versus the alternative hypothesis , where and is the maximum (minimum) of the variances of several normal distributions. Under the null hypothesis a least favorable configuration (LFC) for the maximum F-ratio test to be greater than or equal to a critical value is determined. The result is important for the calculation of the critical value of the test statistic to ensure a specified significance level under the hypothesis. Furthermore, this result may be used to construct lower confidence bounds for the ratio . A numerical procedure to implement the testing procedure is provided.