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Re: Trend analysis with different number of 'PSU' and 'Strata' [message #24602 is a reply to message #24590] Mon, 06 June 2022 16:16 Go to previous messageGo to previous message
Janet-DHS is currently offline  Janet-DHS
Messages: 938
Registered: April 2022
Senior Member
Following is a response from DHS Research & Data Analysis Director, Tom Pullum:

You are correct. Two means (or proportions) can be significantly different even if the confidence intervals overlap. The reason for this is that the standard error of a difference is less than the sum of the two standard errors (the widths of the confidence intervals are proportional to the standard errors). In most situations, the standard error of a difference is equal to the square root of the sum of the squares of the two standard errors. It's like a right triangle, in which the hypotenuse is always shorter than the sum of the other two sides. Check a statistics text on tests and confidence intervals for a difference.

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