= Solution
The <null hypothesis> is that price and score are independent, equivalently that the <independence log-linear model for a two-way contingency table> is correct. Against the saturated alternative, the reported <Poisson deviance> is the <likelihood-ratio test statistic>
$$
G^2=4.6135.
$$
Under the null and the usual large-sample regularity assumptions, <Wilks theorem> gives
$$
G^2\xrightarrow{\mathrm d}\chi^2_{(3-1)(3-1)}=\chi^2_4.
$$
The observations must be independent, the cell probabilities must not lie on the boundary of the parameter space, and the expected counts must be large enough for the <chi-squared asymptotic approximation>. The fitted counts are either $31/3$ or $28/3$, so the customary expected-count check is comfortably satisfied. Since
$$
4.6135<\chi^2_{4,0.99}\simeq13.277
$$
(equivalently, the <p-value> is about $0.329$), we do not reject the null at the $1\%$ <significance level>. The data provide no significant lack of fit for independence.
Back to article page
