Troubleshooting
Problem
An opinion survey was performed and it was noticed that some population subgroups are under represented while others are over represented. How does one calculate weights to correct this condition in SPSS?
Resolving The Problem
All hypothesis testing and confidence interval procedures in SPSS, aside from the SPSS Complex Samples module, are based on the simple random sample (SRS) model, wherein each sampling unit of the population under study is assumed to have the same probability of selection. Serious under/over representation of population strata in a sample is an indication that the SRS model is an inappropriate description of how the sample was obtained, and that a complex sampling model is more appropriate. If this is the case, then the Complex Samples module should be considered.
Having acknowledged this, many survey analysts nevertheless want to develop weighting factors to make their sample 'representative' of the population. Here is how one might proceed. Suppose one considers the population under study to be composed of k mutually exclusive and exhaustive strata S1, S2, . . . , Sk. Thus, each member of the study population is a member of one and only one of the k strata. These strata are known to comprise p1, p2, . . . , pk percent of the population, respectively. Further suppose ni completed surveys have been obtained from I th stratum. Let N = n1 + n2 + . . . + nk. Then, for the I th strata, create a sampling weight equal to N * pi /(100* ni).
For example, if one considers the population to be comprised of four strata that comprise 40%, 20%, 30%, and 10% of the total, and in 1000 completed surveys one obtained 300 cases from stratum 1, 100 from stratum 2, 400 from stratum 3, and 200 from stratum 4, a weight of 1000*40/(100*300) = 1.33 would apply to stratum 1, which was under represented; one of 1000*30/(100*400) = .75 would be used for the overrepresented stratum 3.
Not all SPSS procedures handle fractional weights in the same manner. For examples, see Technotes 1476735, 1480921, and 1592441.
Related Information
Historical Number
25507
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Document Information
Modified date:
16 April 2020
UID
swg21477404