Using Johnson's Transformation With Approximate Test Statistics for the Simple Regression Slope Homogeneity

Abstract

The authors used Johnson's transformation with approximate test statistics to test the homogeneity of simple linear regression slopes when both x_ij and x_ij may have nonnormal distributions and there is Type I heteroscedasticity, Type II heteroscedasticity, or complete heteroscedasticity. The test statistic t was first transformed by Johnson's method for each group to correct the nonnormality and to correct the heteroscedasticity; also an approximate test, such as the Welch test or the DeShon-Alexander test, was applied to test the homogeneity of the regression slopes. Computer simulations showed that the proposed technique can control Type I error rate under various circumstances. Finally, the authors provide an example to demonstrate the calculation.

Key Words:

• Alexander-Govern test
• heteroscedasticity
• Welch test