Mistake Master
An Interval That Contains Zero Has Not Shown the Groups Are Equal
You'll learnto read a direction off a difference interval by locating the WHOLE interval against zero — why an interval containing zero is a failure to decide rather than a finding of equality, why "most of it is positive" measures nothing, why the order of subtraction has to be stated, and how the confidence level can change the answer.
A confidence interval for the difference between two proportions answers one question: is the whole interval on one side of zero? Two checkout systems give (0.018, 0.182) — every value in it is positive, so the new system really does finish more shoppers. Two lecture sections give (−0.022, 0.092), which contains zero, and that is a failure to decide rather than a finding that the sections are equal; 81% of that interval is positive, and 81% establishes nothing at all. A third study runs entirely below zero, and reversing the order of subtraction mirrors it through zero without changing a single fact — which is why a report has to say which group was subtracted from which. And the same checkout data at 99% confidence give (−0.007, 0.207), which contains zero: a stricter standard costs the conclusion. Twelve short steps; press Next for each one.