A large volume of research has focused on comparing the difference between two small binomial proportions. Statisticians recognize that Fisher’s Exact test and Yates chi-square test are excessively conservative. Likewise, many statisticians feel that Pearson’s Chi-square or the likelihood statistic may be inappropriate for small samples. Viable alternatives exist.
Reed, James F. III
"JMASM11: Comparing Two Small Binomial Proportions,"
Journal of Modern Applied Statistical Methods:
1, Article 27.
Available at: http://digitalcommons.wayne.edu/jmasm/vol3/iss1/27