 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2008/o/o1/i/solution

X^{2} = i, j \sum \frac{( O _{ij} - E _{ij} ) ^{2}}{E _{ij}}, E_{ij} = \frac{O _{i +} O _{+ j}}{N} .

Here

O_{i +}, O_{+ j}

are the observed margins and

N

their grand total. Under the independence null, its usual large-sample reference distribution has

(r - 1) (c - 1)

r

-by-

c

table.

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