For a Rasch analysis I have to perform independent t-tests (it’s done to check for unidimensionality). It is expected that 5% of these t-tests will be significant due to chance. Now I get 8 % significant and I want to see, whether 5% are still in the confidence interval (sample size = 100).

I wanted to use the following formula:

0.08 +/- 1.96(sqr root ((0.08*0.92)/100)

Now I checked other papers doing the same (referring to binominal proportions confidence interval), but they seem to use another formula, as I can’t reproduce their CI-findings.

Example:

7.98 % of the t-tests are significant. CI: 4.9 – 11.1. N = 188.

Using the formula from above, I get a CI of 4.11 – 11.85. It could be a mistake of this study, but I had the same problem with two other papers, I could not reproduce their CI-findings.

What am I missing? Am I using the wrong formula, and if so, why? Thanks a lot in advance!