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

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, then the sum

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follows the

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(chi-square) distribution with N degrees of freedom. The

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test compares s with the integral of the

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distribution; if the sum above is equal to the quantile

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of the

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distribution

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then the probability of obtaining s or a larger value in the 'null hypothesis' (i.e. the y_i are drawn from a distribution described by the

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) is given by

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. Integral curves for the

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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

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's. The only statement to make about a measured s is the one above: ``

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is the probability of finding a

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as large as s or larger, in the null hypothesis.

Rudolf K. Bock, Oct 2000