Testing for the equality of the variances of two populations is a classic problem with many not-quite-exact, not-quite-robust, not-quite-powerful-enough solutions. Sukhatme  lists four alternative approaches and adds a fifth of his own; Miller  lists ten alternatives and compares four of these with a new test of his own; Conover, Johnson, and Johnson  list and compare 56 tests; and Balakrishnan and Ma  list and compare nine tests with one of their own.
None of these tests proves satisfactory in all circumstances, for each requires that two or more of the following four conditions be satisfied:
As an example, the first published solution to this classic testing problem is the z-test proposed by Welch  based on the ratio of the two sample variances. If the observations are normally distributed, this ratio has the F-distribution, and the test whose critical values are determined by the F-distribution is uniformly most powerful among all unbiased tests [Lehmann, 1986, Section 5.3]. But with even small deviations from normality, significance levels based on the F-distribution are grossly in error [Lehmann, 1986, Section 5.4].
Box and Anderson ...