Past exam of the probability, statistics and options I course of the University of Oxford / 2008 / O / 1 / i

Table of contents
- Solution i

Solution

For observed counts

O_{ij}

in an

r

by

c

contingency table, Pearson's chi-squared test statistic for independence is

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)

degrees of freedom.

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