A Comparison of Two Noncentral F Approximations, with Applications to Power Analysis in Set Correlation

The preparation of tables for power analysis for set correlation requires the use of the noncentral F distribution for which sufficiently detailed tables are not available. Laubscher (1960) provides approximations based on the square and cube roots. As a basis for a choice between them, we undertook a Monte Carlo investigation of the empirical power of Rao's approximate F test that employed 97 correlation matrices of three sizes and resulted in 521 power determinations, each based on 1000 samples, to which the two approximations could be compared. In addition, a subsample of 205 determinations could be compared with exact power values. Both approximations proved quite adequate, but the square root approximation had a slight edge and was chosen for the computation of the set correlation power tables.