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Hello,

While studying, I came across a question regarding the critical value for the Pearson chi-square test (pg. 1.66) and the LRT (pg. 1.68) for the hypothesis test, testing H0: pi1 - pi2 = 0 vs Ha: pi1 - pi2 ne 0. The Pearson chi-square critical value is chi-square (1, 1 - alpha) while the LRT critical value is chi-square (1, 1 - alpha/2). Why does it appear the Pearson is conducting a one sided test while the LRT appears to be conducting a two sided test?

Thank you!
Emily