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Statistical formula for the chi-square test
The following table shows the notation used in this topic.
Notation
Description
Observed frequency in row i, column j. This value is weighted in a weighted table, unweighted in an unweighted table.
Number of rows contributing to the test.
Number of columns contributing to the test.
The total in row i:
The total in column j:
The total in the table or section of the table being tested:
The expected value in the table or section of the table being tested:
where, for Pearson's formula:
and for the Yates' correction:
The degrees of freedom are:
For details of Fisher's exact test, see Appendix 5, p562-564, SPSS 7.5 Statistical Algorithms (1997), Chicago, IL: SPSS Inc. ISBN 1-56827-185-9.
See also
Example of the chi-square test
Details and restrictions of the chi-square test
Chi-square test