Can you build a confidence interval with only binary data ?

If I know nothing about a process and have only a series with n results of True False. Can I build a 95% probability confidence interval for the true probability of a True, using some kind of assumptions ?

Assuming I understood your question: yes, you can construct a confidence interval for the population proportion of “True” events out of the total.

Here’s a general idea to get you started:

Hope this helps!

yes, you can. for instance, when you do a logistic regression for your binary data, you get this thing called odds ratio after exponentiating your coefficient (see more in Level II) ; For instance, you could say that men are 4 [95% CI: 2-6] times more likely to reads Sports magazine relative to women.

-the 4 represents the estimate from the odds ratio

  • the 95% CI: indicates that the estimate will fall between 2-6 in about 95% of the cases if you used the same number of subjects in order to perform your study

An odds ratio isn’t a probability, though. It’s a ratio of odds, and odds are a ratio of probabilities. I wasn’t sure if the OP wanted to model the probability-- I assumed he had only one variable and wanted a CI for the true proportion of the population with that characteristic.

Edit: completely glossed over a few points before, and I mixed up a few points as a result. Now, the bold has my replies, and I fixed my mistakes…the end of a long day.

Your additions about the CI are correct; the 95% CI will tell us that we expect 95% of the interval estimates to include the true population parameter, if we carried an infinetly many studies. Or another way I’ve seen it often formulated: you are 95% confident that the true mean is between lower-upper interval

That’s essentially what I meant by “there is a 95% level of confidence that the true odds ratio for (whatever it is you’re measuring) will fall between 2 and 6.” We are X% confident that the true parameter value will fall between lower-upperbound (units of measure if applicable)-- almost identical to yours! yes