1. Multiple Indicator Cluster Surveys Data Processing Workshop
Sample Weights
MICS Data Processing Workshop

2. What are sample weights ?
Sample weight: a statistical correction factor used to correct for imperfections in the sample that might lead to bias:
Unequal probabilities of selection
Non-response
Constant sampling weight: self-weighting sample

3. Self-weighting sample
Constant sampling weight: self-weighting sample
Stratum level (e.g., urban and rural within region)
National level: overall self-weighting sample (almost inexistent in household surveys)

4. Self-weighting sample
Advantages
Equally representative for every unit
Reduced sampling errors
Disadvantages:
Difficult for survey management (e.g., to distribute the work-load) because of the variant sample take by PSU
Difficult to control the expected sample size

5. Self-weighting sample
Disadvantages
Self-weighting is not exact because of the rounding of the sample takes and this will bring bias in the survey estimation
In most MICS surveys, if not all, samples are not self-weighting. Therefore, sample weights must be used for reporting national estimates

6. Example - Sample Weights
For example, the weights for North and West regions (Popstan)
North region 10,000/500 = 20
West region 10,000/250 = 40
In North region, each household selected represents 20 households in that region – same figure is 40 in West
Overall, every household selected in Popstan represents households (20,000/750)

7. Example - Sample Weights
In other words, relative to a proportional selection (should be 375 households selected from each region), more households have been selected from North, less have been selected from West
This has to be “compensated” by using sample weights during analysis to re-calibrate the sample to the national level

8. Example - Sample Weights
In our example let’s assume that:
25 percent of households in North use improved water sources
75 percent of households in West use improved water sources
If the sample was selected proportionally (375 households from each region), then our survey estimate would be
((375 * 0.25) + (375 * 0.75)) / 750 = 0.50

9. Example - Sample Weights
If we do not weight, then our national estimate will be
((500 * 0.25) + (250 * 0.75)) / 750 = 0.417
Because, we have over-sampled a region (North region) where use of improved water sources is less
We need to calculate sample weights to “correct” this situation

10. Example - Sample Weights
If we assigned a weight of 20 to each household in North, and 40 to each household in West, this would do the trick
(500 * 20 * 0.25) + (250 * 40 * 0.75)
(500 * 20) + (250 * 40)
= 0.50

11. Example - Sample Weights
This is fine, but SPSS tables would show 20,000 households as the denominator
We do not want this
So, we normalize the weights
We calibrate (normalize) them so that the average of the weights in the data set is equal to 1

12. Example - Sample Weights
The normalized weight for the North region is calculated as (10000/500)/(20000/750) = 0.75
And for the West region, (10000/250)/(20000/750)
= 1.5
When we calculate the national use of improved water sources by using normalized weights,
(500 * 0.75 * 0.25) + (250 * 1.5 * 0.75) 375 =
(500 * 0.75) + (250 * 1.5) 750

13. Sample weights
Based on the design of the sample, there are two (common) approaches to calculating weights:
Each cluster has a unique sample weight (weights.xls)
Each stratum has a unique sample weight (weights_alt.xls)
We have templates for both. You will need to work with your sampling expert to see which one you will use

14. Sample Weights Objects
weights.xls
spreadsheet that calculates weights
weights_table.sps
SPSS program that provides input data for spreadsheet
weights.sps
SPSS program that defines structure of spreadsheet’s output
weights_merge.sps
SPSS program that merges weights onto the MICS data files

15. Calculating sample weights
The spreadsheet weights.xls is used to calculate the sample weights
It has two worksheets, calculations and output.
The calculations worksheet performs the calculations
The output worksheet contains only the sample weights and a list of cluster numbers; format useful for reading the data into SPSS

16. Weights calculation template

17. Calculating and adding sample weights
weights_table.sps produces data needed for calculating the sample weights
weights_merge.sps adds the appropriate sample weights to the analysis files

18. Steps in calculating sample weights
The process of calculating sample weights and adding them to your analysis files can be broken down into six steps

19. Steps in calculating sample weights
Adjust the number of rows in the calculations and output worksheets so that there is one row per cluster in your survey. After you have added or deleted rows, be sure to check that doing so did not affect the totals row in the calculations worksheet

20. Steps in calculating sample weights
Enter required information for columns B to F and for columns H and I

21. Steps in calculating sample weights
Update the definition of strata (or domains) on lines 3 through 10 of the program weights_table.sps
The standard programs assume that strata are formed by all combinations of area (that is, urban and rural) and region and that there are four regions (the program should be modified to reflect the strata or domains in use in your sample)

22. Steps in calculating sample weights
Execute the program weights_table.sps.

23. Steps in calculating sample weights
Copy the information in the table and paste it into the calculations worksheet of weights.xls
When you complete this step, weights.xls will automatically calculate the sample weights

24. Steps in calculating sample weights
Execute the program weights_merge.sps
Once you have completed the sixth step, be sure to check the output list for error messages and to open the analysis files and confirm that the weights have been properly merged