(Binominal proportions) confidence interval – which formula to use?


New Member
Hey, I got a quick question regarding confidence intervals.

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.
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!


Less is more. Stay pure. Stay poor.
See formula 2 in this paper, its the same as your formula. I calculated these as well and got the same as you. I would guess that it may just be rounding errors since they are likely providing rounded decimal places for the publication. Can you generate their data to greater decimals with what is provided in the manuscript?


Or I am missing something as well.
Hey, thanks a lot for the reply and the attached paper. I'm glad to hear that I most probably used the correct formula.
Unfortunately, the generation of data with greater decimals is not possible, that's all I got.
I might simply just ask the authors, because I don’t think that these are rounding errors, the difference is too big I think…
Thanks again! i'd let you know if I get some news...