Efficiency of test for independence after Box–Cox transformation

We consider the efficiency and the power of the normal theory test for independence after a Box–Cox transformation. We obtain an expression for the correlation between the variates after a Box–Cox transformation in terms of the correlation on the normal scale. We discuss the efficiency of test of independence after a Box–Cox transformation and show that for the family considered it is always more efficient to conduct the test of independence based on Pearson correlation coefficient after transformation to normality. Power of test of independence before and after a Box–Cox transformation is studied for a finite sample size using Monte Carlo simulation. Our results show that we can increase the power of the normal-theory test for independence after estimating the transformation parameter from the data. The procedure has application for generating non-negative random variables with prescribed correlation.