Here you can calculate the confidence interval of a proportion (or "risk") by entering the info that you have into the yellow input fields. If you know the
events (or "cases") out of the total sample of size N, then you should choose the option "events and N" in the drop-down selector menu. If, on the other hand, you
already know the proportion and the sample size N, then you choose this option ... etc. You are being given both the approximated confidence interval (using the
z-distribution) as well as the exact confidence interval (using the t-distribution) with the percentage of precision of your choice (the default is 95 %) . If N is
large, the two intervals will differ only slightly. You can test whether the proportion could be lesser than, larger than or equal to a certain, given value by
performing either a z-test or a t-test (or both). If the p-value in the test is below 0.05 then the null hypothesis can be rejected on a 5 % significance level,
namely that the proportion could be either lesser than, greater than or equal to the value that you entered into the null hypothesis input field. The t-test is more
precise, but if N is large the p-values in the two tests will differ only slightly.
For info about the formulas used in the calculations, please see the page medical statistics formulas.