I'm trying to grasp the functional differences between the way SAS calculates its confidence intervals with PROC Surveymeans and a traditional Z-score-based calculation:   PROC Surveymeans produces a wider interval for my data than calculating the interval using the estimated mean, standard error, and Z-score (e.g., ~1.96 for 95%). For reference:  expected 95% CI [44592, 69542] To get the CIs produced by PROC Surveymeans with the Z score method (for this dataset), you would need to use something closer to Z=1.99 rather than 1.96. I found this paper that suggests an adjustment is being applied to CIs produced by PROC Surveymeans to account for unequal weights in the data: https://support.sas.com/resources/papers/proceedings17/0970-2017.pdf. However, the method of adjustment is not detailed therein.  SAS code used to produce these estimates and the CI: proc surveymeans data = DATA nobs sum clsum varsum cvsum nosparse; class DUM; cluster psu; strata stratum; weight wt; var DUM; run;   My questions: Is there information on the correction applied that would cause this difference in CI calculation? The formula used to calculate the bounds of the interval would be ideal. What is the theory/justification behind applying further adjustment to a confidence interval calculation when the error estimates already account for survey design/weights? Thank you! ... View more