Question & Answer
Question
I'm running the CSTABULATE procedure (through Analyze->Complex Samples->Frequencies, or Analyze->Complex Samples->Crosstabs) and requesting percentages, standard errors, and confidence intervals. The confidence intervals do not appear to be simply the estimated proportions plus or minus so many standard errors. How are they computed?
Answer
In order to keep them bounded within the 0-1 (or 0-100 in the percentage metric) range, confidence intervals in CSTABULATE are computed via a logit transformation method, as follows:
1) Transform the estimated proportion p via the logit transformation:
ln(p/(1-p)).
2) Take plus or minus (for upper and lower bounds)
(se/(p*(1-p))) * t-critical(1-alpha/2,df)
where se is the estimated standard error, and t-critical is the value cumulative distribution function of the central t distribution at the chosen alpha level, with degrees of freedom (df) equal to the number of PSUs (primary sampling units) minus the number of strata.
3) Back-transform the interval end points via the inverse logistic transform:
exp(x)/(1+exp(x))
(which is the same as 1/(1+exp(-x)).
Related Information
Historical Number
50346
Was this topic helpful?
Document Information
Modified date:
16 April 2020
UID
swg21480661