Sample Results

Figure 1. Data Editor with sample results
Data Editor with sample results

You can see the sampling results in the newly created dataset. Five new variables were saved to the working file, representing the inclusion probabilities and cumulative sampling weights for each stage, plus the final sampling weights. Voters who were not selected to the sample are excluded from this dataset.

The final sampling weights are identical for voters within the same neighborhood because they are selected according to a simple random sampling method within neighborhoods. However, they are different across neighborhoods within the same township because the sampled proportions are not exactly 20% in all neighborhoods.

Figure 2. Data Editor with sample results
Data Editor with sample results

Unlike voters in the second stage, the first-stage sampling weights are not identical for townships within the same county because they are selected with probability proportional to size.

Figure 3. Joint probabilities file
Joint probabilities file

The file poll_jointprob.sav contains first-stage joint probabilities for selected townships within counties. County is a first-stage stratification variable, and Township is a cluster variable. Combinations of these variables identify all first-stage PSUs uniquely. Unit_No_ labels PSUs within each stratum and is used to match up with Joint_Prob_1_, Joint_Prob_2_, Joint_Prob_3_, Joint_Prob_4_, and Joint_Prob_5_. The first two strata each have 4 PSUs; therefore, the joint inclusion probability matrices are 4×4 for these strata, and the Joint_Prob_5_ column is left empty for these rows. Similarly, strata 3 and 5 have 3×3 joint inclusion probability matrices, and stratum 4 has a 5×5 joint inclusion probability matrix.

The need for a joint probabilities file is seen by perusing the values of the joint inclusion probability matrices. When the sampling method is not a PPS WOR method, the selection of a PSU is independent of the selection of another PSU, and their joint inclusion probability is simply the product of their inclusion probabilities. In contrast, the joint inclusion probability for Townships 9 and 10 of County 1 is approximately 0.11 (see the first case of Joint_Prob_3_ or the third case of Joint_Prob_1_), or less than the product of their individual inclusion probabilities (the product of the first case of Joint_Prob_1_ and the third case of Joint_Prob_3_ is 0.31×0.44=0.1364).

The pollsters will now conduct interviews for the selected sample. Once the results are available, you can process the sample with Complex Samples analysis procedures, using the sampling plan poll.csplan to provide the sampling specifications and poll_jointprob.sav to provide the needed joint inclusion probabilities.