For each cell,

xxx | observed — expected expected |
x 100 |

Thus, a percentage deviation of +15% within a cell indicates that the observed frequency is 15% greater than the expected, while a percentage deviation of -15% indicates that the observed frequency is 15% smaller than the expected.

In the special case of df=1, the calculation of percentage deviation incorporates a correction for continuity:

xxx | |observed — expected| —0.5 expected |
x 100 |

The

xxx | z = | observed — expected sqrt[expected] |

In the special case of df=1, the calculation of the standardized residual incorporates a correction for continuity:

xxx | z = | |observed — expected| —0.5 sqrt[expected] |

The resulting value

The chi-square value that results from a chi-square analysis is equal to the sum of the the squares of the standardized residuals.

Assuming the null hypothesis to be true, and providing that the expected value for a cell is at least 5, values of the standardized residual belong to a normally distributed sampling distribution with a mean of zero and a standard deviation