From the simulation results, we found no significant difference in the performance of test procedures based on
approximate p-value method by substituting the CMLE and substituting the unbiased estimates
Since the computation of CMLE requires to solve a quadratic equation while the unbiased estimate involves a straightforward
calculation only, we will present the result for
First, we compare the test procedures based on their type-I error rate. For the purpose of illustration, we presented
the plots of simulated significance levels for the test procedures against 1 at d = 0.5, 1.0 and 1.5 when = 0.5 in
Fig. 1. We observed that when 1 is small (say 15), most of the test procedures are conservative while some of
the test procedures could produce severely inflated significance