The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective |
| |
Authors: | Gregory Camilli |
| |
Institution: | (1) Rutgers University, 10 Seminary Place, 08903 New Brunswick, NJ |
| |
Abstract: | It is demonstrated in this paper that two major tests for 2 × 2 talbes are highly related from a Bayesian perspective. Although it is well-known that Fisher's exact and Pearson's chi-square tests are asymptotically equivalent, the present analysis shows that a formal similarity also exists in small samples. The key assumption that leads to the resemblance is the presence of a continuous parameter measuring association. In particular, it is shown that Pearson's probability can be obtained by integrating a two-moment approximation to the posterior distribution of the log-odds ratio. Furthermore, Pearson's chi-square test gave an excellent approximation to the actual Bayes probability in all 2×2 tables examined, except for those with extremely disproportionate marginal frequencies. |
| |
Keywords: | 2 × 2 tables four-fold tables Fisher's exact test chi-square test hypergeometric distribution double binomial distribution binary data categorical data Bayes theorem |
本文献已被 SpringerLink 等数据库收录! |
|