Chi-Square Test

  If N measurements y_i are compared to some model or theory predicting values g_i, and if the measurements are assumed normally distributed around g_i, uncorrelated and with variances , then the sum

follows the (chi-square) distribution with N degrees of freedom. The test is said to have the significance level if the sum above is equal to the quantile of the distribution:

Integral curves for the distribution exist in computer libraries or are tabulated in the literature. Note that the test may express little about the inherent assumptions; wrong hypotheses or measurements can, but need not cause large 's. The correct statement to make about a measured s is `` is the probability of finding a as large as s or larger''.