Question

3. Let Yi ~ Binonial(nj:pj), J = 1, 2 independently. For testing the null hypothesis Ho : P1 = P2, a coinmonly used test statistic (slightly different frorn the one given in lecture) s Pi-P2 where pi = Y5/nj and p = (Yİ + Y)/(m + n2) is the pooled estimate of proportion urder Ho. Such data can also be surnmarized as a 2 × 2 table of counts Population Successes Failures Yi 2 For this table, denote the test statistic for the x2 test of homogeneity by X2, that is, x2 = Σί,(Oij-Eij)2/Eij where the surn is over all four cells of the table, Oij is the observed count in cell (i, j), and Eij is the corresponding expected count under Ho. Show that the test based on W is equivalent to Pearson's chi-squared test of homogeneity by proving that W2X2 algebraically.

Answer 1

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