Check the calculations reported in the penultimate paragraph of Sect. 3.4.2 for Bortkewitsch's horsekick data. Compute the row and column totals, and simulate the null distribution of $X^2$ by random matching. Superimpose the ${\chi }_{247}^2$ density on a histogram of the simulated values. Find two positive numbers $a,b$ such that the first two moments of $a{\chi }_b^2$ coincide with the Haldane-Dawson moments. Superimpose this scaled chi-squared density on your histogram. (The intent of this exercise is solely to provide insight into distributional approximation. It should not be read as an endorsement for data analysis.)