# chi-squared test

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- )s^{2}/σ^{ 2},

where

s^{2}is the observed sample variance andσis the standard deviation of the model. Values ofχ^{2}have been tabulated for a range of values ofn, and their distributions (chi-square distributions with (n- 1) degrees of freedom) derived in each case.