Track 7 · Estimation and Confidence Intervals · Lesson 8 of 10
Interval for a difference in proportions
Build and interpret intervals for a difference in proportions with the unpooled Wald method and Newcombe's hybrid score method.
An online shop tests a redesigned checkout on 8 000 visitors against the old one on another 8 000. Version B converts 3.2% of visitors, version A 2.9%. Is B better, or could the gap be noise? The interval for the difference shows both the size of the plausible lift and how uncertain it is.
With two independent groups, the parameter is and its estimate is . Because the groups are independent, the variances add, and each group's variance uses its own proportion:
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Build a Wald interval for a difference in proportions with the unpooled standard error
- Explain why tests pool and intervals do not
- Assemble Newcombe's interval from two Wilson intervals, and prefer it for small counts
- Report a difference in percentage points and interpret an interval that contains 0