A Monte Carlo Investigation of the Box—Cox Transformation in Small Samples

The small-sample properties of models which transform both the dependent and independent variables using the same Box-Cox transformation are investigated in sampling experiments. Bias does not appear to be a serious problem; however, the sign and size of the transformation parameter, which changes the coefficient of variation of the dependent variable, seriously affects the variances of the estimators. Hypothesis tests reveal that t statistics frequently lead to incorrect decisions since the actual sampling distributions have heavier tail areas than the t distribution.