This example is taken from Levy and Lemeshow’s

Sampling of Populations.

page 138 stratified random sampling

The SAS data set wvhospsamp is used in the example. Please note that some modifications were made to the hospsamp data set provided by Levy and Lemeshow to facilitate the analysis in WesVar. While the data were still in SAS, a variable called

psuwas added. This variable was created using the following SAS code:

data wvhospsamp; set hospsamp; psu = _n_; if oblevel = 2 then psu = psu - 4; if oblevel = 3 then psu = psu - 9; run;

The point of this code is to create a new variable, that we called

psu, that counts each observation within each level of the variableoblevel. This is necessary for analysis in WesVar. Ifpsuwas not consecutive numbers starting from 1 within each level ofoblevel, WesVar would give an error message and the analysis could not be completed. Because the sampling rate is different within the levels ofoblevel, we must use the “Attach Factors” feature of WesVar to give the appropriate FPCs for each level ofoblevel. To calculate each FPC, use the formula 1 – (n/N), where n is the size of the sample and N is the size of the population. Hence, the calculation for level 1 ofoblevelwould be 1 – (4/42) = .9047619; for level 2, 1 – (5/99) = .949495, for level 3, 1 – (6/17) = .64705882. While calculations to this many decimal places is not required, rounding to two or three decimal places will slightly alter the results. Also note that, in the “movie”, when WesVar asks about saving the FPCs to an external data file, we decline. In many situations it may be a good idea to save the FPCs for future use or reference.

In this example, the variable

weightais used as the weight variable, the variablepsuis used as the VarUnit, the variableoblevelis used as the VarStrat and the variablebirthsis used as the analysis variable. The jackknife-n (jkn) method of creating the replicate weight is used because we do not always have exactly two PSUs per stratum in this design. The table is created usingoblevelbybirthsto give all of the information shown in the text (but it is still a “single” table).

Part of the output is given below. Because the output is extensive, only part of it is shown as it appears in WesVar. For the rest of the output, the export function was used to export the output to a text file. This text file was edited to show only the relevant values.

NUMBER OF REPLICATES : 15 NUMBER OF OBSERVATIONS READ : 15 WEIGHTED NUMBER OF OBSERVATIONS READ : 158.000 TABLE : OBLEVEL * BIRTHS OBLEVEL BIRTHS STATISTIC EST_TYPE ESTIMATE STDERROR CELL_n 1 MARGINAL SUM_WTS VALUE 42.0000 0.0000 4 2 MARGINAL SUM_WTS VALUE 98.9999 0.0000 5 3 MARGINAL SUM_WTS VALUE 17.0000 0.0000 6 MARGINAL MARGINAL SUM_WTS VALUE 157.99990.0000151 MARGINAL BIRTHS VALUE 4931.0000 2669.8567 4 2 MARGINAL BIRTHS VALUE 117116.9278 33067.6649 5 3 MARGINAL BIRTHS VALUE 51934.9767 7508.3982 6 MARGINAL MARGINAL BIRTHS VALUE 183982.904534014.3300 15 1 MARGINAL mean VALUE 355.5000 63.5680 4 2 MARGINAL mean VALUE 1183.0000 334.0170 5 3 MARGINAL mean VALUE 3055.0000 441.6707 6 MARGINAL MARGINAL mean VALUE 1164.4493215.2807 15

The value 57.9999 (with bolding added) indicates that there are approximately 158 weighted observations in the data set, which is consistent with the note above in the text output. The 15 in the same row in the column CELL_n indicates that there are 15 unweighted observations in the data set. The totals and the corresponding standard errors for the three levels of

oblevelare given in the next three rows of the table. The grand total of 183982.9045 (with bolding added) is given in the next line. The means and corresponding standard errors forbirthsfor each level ofoblevelare given in the next three rows of the text output, and the grand mean of 1164.4493 (with bolding added) is given in the last row of the table.

This example is taken from Lehtonen and Pahkinen’s

Practical Methods for Design and Analysis of Complex Surveys.

page 74 Table 3.2 An optimally allocated stratified simple random sample from the Province’91 data set.

The SAS data set for this example can be downloaded by clicking here. Note that the different FPCs for the two strata need to be entered in the “Attach Factors” window. This is done after the replicate weights are created but while you are still in the create data set window. From the “Data” pull-down menu at the top of the screen, select “Attach Factors”. For strata 1 (cases 1 through 4), the FPC is 1 – (4/7) = .43. For strata 2 (cases 5 through 8), the FPC is 1 – (4/25) = .84.

In this example, the variable

wtis used as the weight variable, the variablepsuis used as the VarUnit, the variablestris used as the VarStrat and the variableue91is used as the analysis variable.

Part of the output is given below.

The marginal sum_wts value of 32 is the estimated population total. The marginal ue91 value of 15210.5 is the estimated total of the variable ue91, and its standard error is 4285.7249. The marginal ratio value of 0.1278 is the estimated ratio of ue91/lab91, and its standard error is 0.0037. The output regarding the median has been omitted. The results from WesVar differ from those given in the text. We suspect that this is due to a difference in the algorithms used by the different statistical packages.