Table : TABLE 12-14. The Bonferroni Test: Few Groups, Many Comparisons Even with a few means, we must make many comparisons to account for every possible difference. Because we run the risk of incorrectly rejecting the null hypothesis just by chance if we run so many tests, it is a wise idea to use a more conservative procedure, such as the Bonferroni test, when comparing means. The Bonferroni test requires that we divide an overall p level, such as 0.05, by the number of comparisons we will make.