Let Y i be a bin(n i , i ) variate for group i, i 1, N, with Yi independent Consider the model that 1 N Denote that common value by For observations y i show that (y i ) (n i ) When all n i 1, for testing this models fit in the N 2 table, show that X 2 n Thus, goodness of fit statistics can be completely uninformative for ungrouped data

Question: Let Y i be a bin(n i , i ) variate for group i, i = 1, ...... N, with {Yi} independent. Consider the

Let Y_i be a bin(n_i, π_i) variate for group i, i = 1, ...... N, with {Yi} independent. Consider the model that π₁ = .... = π_N. Denote that common value by π. For observations {y_i} show that π̂ = (∑y_i)/(∑n_i).

When all n_i = 1, for testing this model’s fit in the N × 2 table, show that X² = n. Thus, goodness-of-fit statistics can be completely uninformative for ungrouped data.

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