Question 340:

Asked on August 12, 2008

1

Answer:

No answer provided yet.

So it turns out that the reason for the difference is that when there are either all successes or all failures, as is the case in the example I gave (5/5), you cannot have a 2-sided confidence interval (since you can't go above 100%). In these situations a 95% CI ends up being a 97.5% CI. With a 95% interval, there is a 2.5% likelihood of the population completion rate being above this upper-bound or a 2.5% chance of it being below the level. When all pass or fail a task you only have 2.5% below, so you need to use the critical value for a 90% Confidence Level so there is 5% above and 5% below the interval, with the top again getting excluded, leaving you with just 5% below the interval.

There is already a note on the confidence interval calculator page, but that doesn't help while you're reading the Restoring Confidence article. You will notice when you change the Confidence Level to 90% on the calculator or spreadsheet, you'll get 55%.