In a stratified sampling design, when the sampling fraction is the same in all strata, the population mean estimate y is the same as the stratified sampling estimate y_st. Because PROC SURVEYMEANS assigns equal weights of 1 to all observations by default, the sample mean is computed as y even under a stratified design. In order to compute y_st, the appropriate weight variable must be used. If the STRATA statement is specified without a WEIGHT statement, PROC SURVEYMEANS issues the following message:

The following demonstrates the issue using the example titled "Stratified Cluster Sample Design" in the PROC SURVEYMEANS documentation. In the data, there is ice cream spending data from three strata: Grade=7, 8, and 9.

Based on the total number of students in each stratum, the TOTAL= data set is as follows:

The sampling rate in each stratum is as follows:

In order to compute an unbiased estimate for y_st, each observation needs to be weighted appropriately. In this case, the weights are obtained as the ratio of the overall sampling rate (40/4000=0.01) to the sampling rate for the stratum to which this observation belongs. The weights would be constructed as follows:

The following statements estimate the stratified sample mean y_st.

Reference

Cochran, W. G. 1977. Sampling Techniques. New York: John Wiley & Sons.

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