78 CHAPTER 5 Is There a Statistical Difference between Designs? Two-proportion Test Another common way for comparing two proportions is the two-proportion test. It is mathemati- cally equivalent to the chi-square test. Agresti and Franklin (2007) have suggested a rule of thumb for its minimum sample size that there should be at least 10 successes and 10 failures in each sample. It generates a test statistic that is looked up using the normal (z) distribution to find the p-values. It uses the following formula and will be further discussed in a subsequent section ("N - 1 Two- proportion Test"). ð^ 1 - ^ 2 Þ p p z = s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 PQ × + n 1 n 2 Fisher Exact Test The Fisher exact test uses exact probabilities instead of approximations as is done with the chi- square distribution and t-distributions. As with the exact binomial confidence interval method used in Chapter 4, exact methods tend to be conservative and generate p-values that are higher than they should be and therefore require larger differences between groups to achieve statistical