The SURVEYFREQ Procedure

Expected Weighted Frequency

If you specify the EXPECTED option in the TABLES statement, PROC SURVEYFREQ computes expected weighted frequencies for the table cells in two-way tables. The expected weighted frequencies are computed under the null hypothesis that the row and column variables are independent. The expected weighted frequency for table cell (r, c) is

upper E Subscript r c Baseline equals ModifyingAbove upper N With caret Subscript r dot Baseline ModifyingAbove upper N With caret Subscript dot c Baseline slash ModifyingAbove upper N With caret

where ModifyingAbove upper N With caret Subscript r dot is the estimated total for row r, ModifyingAbove upper N With caret Subscript dot c is the estimated total for column c, and ModifyingAbove upper N With caret is the estimated overall total. Equivalently, the expected weighted frequency can be expressed as

upper E Subscript r c Baseline equals ModifyingAbove upper P With caret Subscript r dot Baseline ModifyingAbove upper P With caret Subscript dot c Baseline ModifyingAbove upper N With caret

These expected values are used in the design-based chi-square tests of independence, as described in the sections Rao-Scott Chi-Square Test and Wald Chi-Square Test.

Last updated: December 09, 2022