Power Comparison of Correlation Tests in PASS

When considering the strength of association between two variables, the underlying bi-variate distribution is not always known.
The Power Comparison of Correlation Tests procedure in PASS uses simulation to compare power and alpha for 3 common correlation test procedures.
The three tests that are compared in this procedure are
Pearson’s Correlation Test
Spearman’s Rank Correlation Test
(and) Kendall’s Tau Correlation Test
These last two tests are non-parametric tests.
Suppose a study will be run to test whether the correlation between forced vital capacity (X), and forced expiratory value (Y), in a particular population, is non-zero.
Researchers wish to find the power if the underlying correlation is 0.2 or 0.3, alpha is 0.05, and for sample sizes of 40, 60, 80, 100, and 120.
The first power comparison is made with the assumption of a Bivariate Normal distribution.

For underlying correlations of both 0.2 and 0.3, the Pearson test has a higher power.

A second power comparison is made, with the same assumed correlations, but where a custom bivariate distribution is assumed, with Exponential Marginal distributions.

In this case, the two non-parametric tests have much higher power.