Mistake Master
An Interval That Contains Zero Has Not Shown the Groups Are Equal
You'll learnhow to judge a claim about two population proportions from a confidence interval for their difference: what entirely above or below zero establishes, why containing zero is a failure to decide rather than a finding of equality, and why the sign of the endpoints means nothing until the order of subtraction is written down.
For a difference of two proportions, one value carries all the weight: zero, the claim that the two population proportions are equal. This page builds three intervals from their raw counts and holds each against the same dashed line. A checkout study's interval lands entirely above zero, so a direction is established and a magnitude comes with it. A second study's interval straddles zero — and 81% of its length is positive, which decides exactly nothing, because a negative difference is still inside. A third study's interval sits entirely below zero, until the order of subtraction is reversed and the same finding prints with both signs flipped. And the first study is run once more at 99% confidence, where the same data produce a wider interval that zero has crept into: the direction was real at one standard of evidence and unavailable at a stricter one.