One of the variance reduction methods in simulation experiments is negative correlation induction, and in particular, the use of the antithetic variates. The simultaneous use of antithetic variates and an acceptance-rejection method has been studied in some papers, where the inducted negative correlation has been calculated. In this study, the factors affecting the inducted negative correlation rate are addressed. To do this, the beta distribution is first selected to generate negatively-correlated random variates using the acceptance-rejection methods. The effects of both the efficiency of the acceptance-rejection method and the initial negative correlation rate on the inducted negative correlation are then explored. Results show that both factors have significant effects; therefore, a combination of both can lead to algorithms better able to generate negative correlations.