The Taylor series linearization method can be used to estimate standard errors of proportions and other statistics for crosstabulation tables. For sample survey data, the proportion estimator is a ratio estimator formed from estimators of totals. For example, to estimate the proportion in a crosstabulation table cell, the procedure uses the ratio of the estimator of the cell total frequency to the estimator of the overall population total, where these totals are linear statistics computed from the survey data. The Taylor series expansion method obtains a first-order linear approximation for the ratio estimator and then uses the variance estimate for this approximation to estimate the variance of the estimate itself (Woodruff 1971; Fuller 1975). For more information about Taylor series variance estimation for sample survey data, see Lohr (2010), Wolter (2007), Särndal, Swensson, and Wretman (1992), and Lee, Forthofer, and Lorimor (1989).
When there are clusters (PSUs) in the sample design, the Taylor series method estimates variance from the variance among PSUs. When the design is stratified, the procedure combines stratum variance estimates to compute the overall variance estimate. For a multistage sample design, the variance estimation depends only on the first stage of the sample design. Therefore, the required input includes only first-stage cluster (PSU) and first-stage stratum identification. You do not need to input design information about any additional stages of sampling. This variance estimation method assumes that the first-stage sampling fraction is small, or the first-stage sample is drawn with replacement, as it often is in practice.
For more information about Taylor series variance estimation, see the sections Proportions, Row and Column Proportions, Risks and Risk Difference, and Odds Ratio and Relative Risks.