Conditional significance in the test of the difference between two proportions in small samples  [presentation, pdf, 1375 kB]

Gori F., Grassi M.
First author's affiliation: Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università "La Sapienza", Roma, Italy

When hypotheses concerning difference between proportions are at stake, the significance test is performed on the variable p₁-p₂, which for sufficiently large samples approaches the normal distribution. The reliance on this test seems problematic when sample sizes, n₁ and n₂, are unequal, particularly as n becomes smaller and the values of parameter P are very different from 0.5. In addition, although the study of sampling with replacement is useful for theoretical purpose, in practice researchers rarely use extraction with replacement when small samples are used (as is often the case in psychological research). In this study, a (programmed) solution based upon the exact distribution of the two independent samples in their whole universe is illustrated. Final remarks about the conditional significance and the experimental model are carried out.