Lesson 31 of 1524
Hypothesis testing with two samples
Matched pairs are analyzed as one sample of differences.
Practice this chapterTwo groups are independent when no observation in one is paired with an observation in the other. Separate groups use a two-mean or two-proportion procedure.
Before-and-after measurements on the same people are matched pairs. You subtract within each pair and then run a one-sample test on the differences. The usual null says the mean difference is 0.
A paired estimate
d̄ estimates μd
The average of the paired differences estimates the population mean difference.
Worked example
Five people are weighed before and after a program. The five differences average 2 pounds. What does that 2 estimate?
- 1The same five people were measured twice. Each person gives one pair, so the two measurements are not two independent groups.
- 2Subtract within each pair. That produces five differences, and those five numbers are one sample.
- 3Their average is 2 pounds. A sample mean estimates the matching population mean.
- 4Here the sample mean is the mean of the differences, so 2 estimates μd, the population mean difference.
Result: 2 estimates μd, the mean of the paired differences
Why. The pairing turns two measurements per person into one difference per person. The average of those differences estimates the average difference in the population. It is not an estimate of either group’s mean weight by itself.
Do not treat before-and-after measurements as two independent samples. The pairing is the point of the design.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.