2w This fact resolves a difficulty which has been felt with respect to the fourfold table. In 1915 Greenwood and Yule (3), using four-fold tables to test the effect of inoculation against typhoid and cholera, follow Pearson in applying Elderton's table with n'= 4. They notice, however, that if we calculate the proportion attackedI amiiongi the inoculated and among the uninoculated, thus a, _ c a+ b'e+ d'then the difference p'-p, colmpared to also give a test of independence; the deviations which judged by the x2 test are not improbable, seem much less likely to occur when judged by the proportions attacked. While pointing out the difficulty, these authors judge it safer to apply the x2 test.