Matched Pairs

Matched Pairs for Two Dependent Means

How are two means dependent?

1. One sample is drawn from the same population.
2. Each observation contains a pair of measurements.
3. We assess the differences from the matched or paired samples.

• Since each observation is measured twice, we calculate the difference between the before value and the after value.
• $\overline{d}=\overline{x}_{1i}-\overline{x}_{2i}$
• where $\overline{d}$ is the sample mean of the differences which is the point estimate for the parameter $µ_d$ the population mean of the differences.
• The differences calculated become a single sample, and we can essentially follow the one-sample hypothesis T-test.
• We also have $s_d$, which is the sample standard deviation of the differences.

• The difference in responses of each subject is measured before and after receiving a treatment.
• The difference in the midterm grade and final exam grade of each student is being compared.
• The difference in appraisal value of each used car between two vehicle appraisal companies.

Does Central Limit Theorem apply with matched pairs?

• The matched pairs have differences that is drawn from a population with a normal distribution; or
• The sample size of matched pairs is sufficiently large