The chi-squared test is a test of the closeness of an observed result to the expected result, and hence how closely a model corresponds to a particular sample of n members of a population. χ 2 is given by
χ 2 = (n - )s2/σ 2,
where s2 is the observed sample variance and σ is the standard deviation of the model. Values of χ 2 have been tabulated for a range of values of n, and their distributions (chi-square distributions with (n - 1) degrees of freedom) derived in each case.