TITLE:
Exact Distribution of Difference of Two Sample Proportions and Its Inferences
AUTHORS:
Keshab R. Dahal, Mohamed Amezziane
KEYWORDS:
Statistical Inferences, Exact Distribution, Difference of Sample Proportions
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.3,
May
9,
2020
ABSTRACT: Comparing two population proportions using
confidence interval could be misleading in many cases, such as the sample size being small and the test being based on normal approximation. In this case, the only one 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 and 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 requirements, and can be used to perform
inferences such as: a hypothesis test for
two population proportions, regardless of the nature of the distribution and
the sample sizes. We claim that exact
distribution has the least confidence
width among Wald, Agresti-Caffo and Score, so it is suitable for inferences of the difference between the
population proportion regardless of sample size.