PROC SURVEYMEANS: Definitions and Notation :: SAS/STAT(R) 9.3 User's Guide

Definitions and Notation

For a stratified clustered sample design, together with the sampling weights, the sample can be represented by an $\text{[math]}$ matrix

	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

where

$\text{[math]}$ is the stratum index
$\text{[math]}$ is the cluster index within stratum $\text{[math]}$
$\text{[math]}$ is the unit index within cluster $\text{[math]}$ of stratum $\text{[math]}$
$\text{[math]}$ is the analysis variable number, with a total of $\text{[math]}$ variables
$\text{[math]}$ is the total number of observations in the sample
$\text{[math]}$ denotes the sampling weight for unit $\text{[math]}$ in cluster $\text{[math]}$ of stratum $\text{[math]}$
$\text{[math]}$ are the observed values of the analysis variables for unit $\text{[math]}$ in cluster $\text{[math]}$ of stratum $\text{[math]}$ , including both the values of numerical variables and the values of indicator variables for levels of categorical variables.

For a categorical variable $\text{[math]}$ , let $\text{[math]}$ denote the number of levels of $\text{[math]}$ , and denote the level values as $\text{[math]}$ . Let $\text{[math]}$ $\text{[math]}$ be an indicator variable for the category $\text{[math]}$ $\text{[math]}$ with the observed value in unit $\text{[math]}$ in cluster $\text{[math]}$ of stratum $\text{[math]}$ :

$\text{[math]}$

Note that the indicator variable $\text{[math]}$ is set to missing when $\text{[math]}$ is missing. Therefore, the total number of analysis variables, $\text{[math]}$ , is the total number of numerical variables plus the total number of levels of all categorical variables.

The sampling rate $\text{[math]}$ for stratum $\text{[math]}$ , which is used in Taylor series variance estimation, is the fraction of first-stage units (PSUs) selected for the sample. You can use the TOTAL= or RATE= option to input population totals or sampling rates. See the section Specification of Population Totals and Sampling Rates for details. If you input stratum totals, PROC SURVEYMEANS computes $\text{[math]}$ as the ratio of the stratum sample size to the stratum total. If you input stratum sampling rates, PROC SURVEYMEANS uses these values directly for $\text{[math]}$ . If you do not specify the TOTAL= or RATE= option, then the procedure assumes that the stratum sampling rates $\text{[math]}$ are negligible, and a finite population correction is not used when computing variances. Replication methods specified by the VARMETHOD=BRR or the VARMETHOD=JACKKNIFE option do not use this finite population correction $\text{[math]}$ .

The SURVEYMEANS Procedure

Definitions and Notation