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) equals
![\[ E_{rc} = \widehat{N}_{r \cdot } ~ \widehat{N}_{\cdot c} ~ / ~ \widehat{N} \]](images/statug_surveyfreq0171.png){kind=small} |
where 
is the estimated total for row r, 
is the estimated total for column c, and 
is the estimated overall total. Equivalently, the expected weighted frequency can be expressed as
![\[ E_{rc} = \widehat{P}_{r \cdot } ~ \widehat{P}_{\cdot c} ~ \widehat{N} \]](images/statug_surveyfreq0175.png){kind=small} |
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.