# <u>Post-Stratification</u>

Post-stratification adjustment matches population/household shares of subnational units between a phone survey and a nationally representative reference survey. If some subnational household shares are largely different from the nationally representative reference survey, even if SWIFT poverty estimation is accurate at the subnational levels, the aggregates or the national average poverty rates could differ largely. PSW cannot fully address these differences-even if subnational level indicators have been included in the PSW procedure, the shares of some subnational units may still exhibit non-negligible differences between the two surveys. Poststratification, on the other hand, modifies weights so that the population or household share of each subnational unit is exactly matched between the phone survey and the reference survey.

Under the circumstance that maxentropy or raking is executed at the national level and where subnational household or population shares are included as part of the constraints, post-stratification is not necessary. This is because national-level maxentropy or raking matches the subnational shares by including subnational unit indicators. In contrast, if maxentropy or raking is conducted at a subnational level (within each subnational unit), the adjusted household share of each unit will not be matched to that of the reference survey. Therefore, it is important to implement post-stratification after subnational level maxentropy or raking to eliminate any remaining bias due to mismatched population/household shares.

_Table 1 Post-Stratification Illustrative Example_

|**Reference Survey Hou**|**sehold Distribution**|**Phone Survey House**|**hold Distribution**|
|---|---|---|---|
|District 1|P1|District 1|S1|
|District 2|P2|District 2|S2|
|District 3|P3|District 3|S3|
|District 4|P4|District 4|S4|
|District 5|P5|District 5|S5|
|District 6|P6|District 6|S6|
|District 7|P7|District 7|S7|

Table 1 illustrates an example of post-stratification. Suppose our study setting consists of seven districts (District 1 – District 7), with household totals being P1 to P7, respectively, in the reference survey (Panel 1) and S1 to S7 in the phone survey (Panel 2). A district defines a cell in both panels.

A cell weighting or weighting class approach assigns a weight to each cell in the phone sample so that the weighted total within each cell is identical to the reference survey. In list-based or RDD designs, where households (respondents) are selected with simple random sampling, the weighted total is simply the count of observations. In scenarios where initial weights are available, the original weights, together with any weights applied to compensate for subsampling, are carried over to the new survey sample. The sum of these weights is used as the total number of observations within a sample cell.

Let’s first assume that the phone survey is a simple random sample. To match the distribution of households across regions between the phone and reference surveys, a factor needs to be applied to all observations of the phone survey sample when producing weights. For example, all observations in the cell of District 1 from the phone survey need to be assigned a weight of (P1/S1), all observations in the cell of District 2 (P2/S2), and the same rule applies to all remaining districts. After this post-stratification exercise, the weighted household distribution across all seven districts became identical to the reference survey. If, in contrast, the phone survey is a subsample of an existing survey with initial weights, then rather than use the factor _per se_ as weights, the final weights should be calculated as the product of initial weights and the factor.

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