If two samples are drawn from two independent binomially distributed populations, respectively; to test the significance of the difference between the population proportions, and to determine the power of the test; the pooled estimate of the standard error of the difference of population proportions has been used under the null hypothesis  But this consideration does not leave any room for accommodating the difference when  is true. Now, the core question in researchers’ mind that, whether the consideration of unpooled estimate of standard error of the proportion difference can take care of the situation by accommodating the proportion difference. To resolve the issue, a simulated study has been carried out by using different sample sizes for equal and unequal sample size relationships; and different values of the difference between two proportions. To assess the effectiveness of pooled and unpooled approaches, p-values and test powers have been calculated in this study and compared with the threshold values of 0.05 for the p-value and 80% for the power. It has been found that unpooled approach is more effective for      and  with any  0.10, 0.15, 0.20 and 0.25; and for  with the largest D. More obviously, positive relationship has been observed between effect sizes and test powers but there is an inverse relationship between effect sizes and p-values.

binomial population, effect size, p-value, pooled standard error, test power, unpooled standard error.