Analysis of the Constancy of Error Variance in A Regression Model

Models that specify a constant variance for the error terms perhaps form the “backbone” of statistical modeling as applied to much of scientific investigation. Error variance estimation is one of the most important issues in regression models. The estimation of the error variance is essential to assess the variability of the estimated mean of Y_i given X_i­. Therefore, the error variance plays an important role in regression analysis but uncorrelated in sense that errors in successive measurements cannot be forecast from a knowledge of errors in previous measurements. One of the central messages of this study is that (a) unequal variances may be more prevalent than typically recognized in statistical analysis, and (b) the usefulness of “Levene’s test when considering tests of equal variances, as test is actually a family of techniques. Depending on which of the Levene tests that are being implemented, and particularly the Levene’s test based on means which is found in widely used software like SPSS, one may be using a statistical technique that is as bad (if not worse) than the F test which the Levene test was intended to replace. The primary goals of this study are to (a) demonstrate that the current statistical practice of testing for equality of variances in hypothesis testing (as prescribed by textbooks and statistical software programs) is insufficient, hence data transformation is suggested.

Keywords: Constant variance, Error variance, Estimation, Levene’s test, F-test, transformation.