Hypothesis testing in models using the box-cox transformation

The small sample powers of two statistics, the likelihood ratio test, and a test based on the asymptotic normality of maximum likelihood estimators (z-test) were compared in a simulation experiment. Two models were specified, one containing the Box-Cox transformation on the dependent variable only, and one containing the Box Cox transformation on both the dependent and independent variables. The transformation parameter,λ was estimated 200 times, for each of six different values of z in each of three sample sizes foi both models. At each replication. 17 hypotheses were tested using both a likelihood ratio test and a z-test. Results indicate that w hiic both likelihood ratio tests and z-tests are unbiased, in small samples the z-test is generally preferable to the likelihood ratio test.