Comparing two population proportions using confidence interval could be misleading in many cases, such </span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> the sample size </span><span style="font-family:Verdana;">being</span><span style="font-family:Verdana;"> small and the test </span><span style="font-family:Verdana;">being</span><span style="font-family:Verdana;"> based on normal approximation. In this case, the only </span><span style="font-family:Verdana;">one</span><span style="font-family:Verdana;"> option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any </span><span style="font-family:Verdana;">requirements,</span><span style="font-family:Verdana;"> and can be used to perform inferences such </span><span style="font-family:Verdana;">as:</span><span style="font-family:Verdana;"> a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim </span><span style="font-family:Verdana;">that</span><span style="font-family:Verdana;"> exact distribution has the </span><span style="font-family:Verdana;">least</span><span style="font-family:Verdana;"> confidence width among Wald, Agresti-Caffo </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> Score, so it is suitable for inferences of the difference between the pop