 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2008/o/1/i/solution

For observed counts

O_{ij}

in an

r

c

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

Under the null model and the usual large-expected-count conditions, its reference distribution is

χ^{2}

with

(r - 1) (c - 1)

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