The SURVEYFREQ Procedure

Totals

PROC SURVEYFREQ estimates population frequency totals for the specified crosstabulation tables, including totals for two-way table cells, rows, columns, and overall totals. The procedure computes the estimate of the total frequency in table cell (r,c) as the weighted frequency sum,

ModifyingAbove upper N With caret Subscript r c Baseline equals sigma-summation Underscript h equals 1 Overscript upper H Endscripts sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts sigma-summation Underscript j equals 1 Overscript m Subscript h i Baseline Endscripts delta Subscript h i j Baseline left-parenthesis r comma c right-parenthesis upper W Subscript h i j Baseline

Similarly, PROC SURVEYFREQ computes estimates of row totals, column totals, and overall totals as

ModifyingAbove upper N With caret Subscript r dot Baseline equals sigma-summation Underscript h equals 1 Overscript upper H Endscripts sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts sigma-summation Underscript j equals 1 Overscript m Subscript h i Baseline Endscripts delta Subscript h i j Baseline left-parenthesis r dot right-parenthesis upper W Subscript h i j Baseline
ModifyingAbove upper N With caret Subscript dot c Baseline equals sigma-summation Underscript h equals 1 Overscript upper H Endscripts sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts sigma-summation Underscript j equals 1 Overscript m Subscript h i Baseline Endscripts delta Subscript h i j Baseline left-parenthesis dot c right-parenthesis upper W Subscript h i j Baseline
ModifyingAbove upper N With caret equals sigma-summation Underscript h equals 1 Overscript upper H Endscripts sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts sigma-summation Underscript j equals 1 Overscript m Subscript h i Baseline Endscripts upper W Subscript h i j Baseline

PROC SURVEYFREQ estimates the variances of totals by using the variance estimation method that you request. If you request a replication method (bootstrap, BRR, jackknife, or replicate weights), the procedure estimates the variances as described in the section Replication Variance Estimation.

By default, PROC SURVEYFREQ estimates variances by using the Taylor series method (which you can also request by specifying the VARMETHOD=TAYLOR option). Because totals are linear statistics, their variances can be estimated directly, without the approximation that is used for proportions and other nonlinear statistics. PROC SURVEYFREQ estimates the variance of the total frequency in table cell (r, c) as

ModifyingAbove normal upper V normal a normal r With caret left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline right-parenthesis equals sigma-summation Underscript h equals 1 Overscript upper H Endscripts ModifyingAbove normal upper V normal a normal r With caret Subscript h Baseline left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline right-parenthesis

where if n Subscript h Baseline greater-than 1,

StartLayout 1st Row 1st Column ModifyingAbove normal upper V normal a normal r With caret Subscript h Baseline left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline right-parenthesis 2nd Column equals 3rd Column StartFraction n Subscript h Baseline left-parenthesis 1 minus f Subscript h Baseline right-parenthesis Over n Subscript h Baseline minus 1 EndFraction sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts left-parenthesis n Subscript r c Superscript h i Baseline minus n overbar Subscript r c Superscript h Baseline right-parenthesis squared 2nd Row 1st Column n Subscript r c Superscript h i 2nd Column equals 3rd Column sigma-summation Underscript j equals 1 Overscript m Subscript h i Baseline Endscripts delta Subscript h i j Baseline left-parenthesis r comma c right-parenthesis upper W Subscript h i j Baseline 3rd Row 1st Column n overbar Subscript r c Superscript h 2nd Column equals 3rd Column left-parenthesis sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts n Subscript r c Superscript h i Baseline right-parenthesis slash n Subscript h Baseline EndLayout

and if n Subscript h Baseline equals 1,

ModifyingAbove normal upper V normal a normal r With caret Subscript h Baseline left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column normal m normal i normal s normal s normal i normal n normal g 2nd Column if n Subscript h Sub Superscript prime Subscript Baseline equals 1 for h prime equals 1 comma 2 comma ellipsis comma upper H 2nd Row 1st Column 0 2nd Column if n Subscript h Sub Superscript prime Subscript Baseline greater-than 1 for some 1 less-than-or-equal-to h prime less-than-or-equal-to upper H EndLayout

The standard error of the total is computed as

normal upper S normal t normal d normal upper E normal r normal r left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline right-parenthesis equals StartRoot ModifyingAbove normal upper V normal a normal r With caret left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline right-parenthesis EndRoot

The variances and standard errors are computed in a similar manner for row totals, column totals, and overall table totals.

Last updated: December 09, 2022