This article deals with the problem of testing the variances of two normal populations under the assumption that the mean parameters are equal. We propose an approximate likelihood ratio test and a test based on bootstrap observations. Two computational approach tests are suggested using the maximum likelihood estimators of the model parameters. Further, several generalized test methods are discussed to test the variances. Through a detailed Monte Carlo simulation study, the performances of the proposed test procedures are compared numerically in terms of their sizes and powers. Finally, we present real-life data sets to demonstrate the potential applicability of the suggested test procedures.
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