9-4 Testing Paired Differences (dependent samples)

Paired Data Before/After Twins Left and right arm (foot, leg, eyes..) of the same person Obviously, these are not independent. Therefore, two sample t can’t be used. Checking differences is the way to go. Paired data controls for unexpected, extraneous factors. Want to make a claim about the health benefits of a fish food? If you want the study to carry some weight, you should pair the same type of fish (and perhaps even gender…)

Paired Data (continued) Since we can’t use the two sample t test, instead treat the difference as the data of interest. Remember – before/after is NOT independent.

Test Statistic For paired differences, the difference d of the data pairs is measured against the sample mean difference d.

Test Statistic For paired differences, the difference d of the data pairs is measured against the sample mean difference d. The null hypothesis is that Right tailedleft tailed two tailed

Test Statistic For paired differences, the difference d of the data pairs is measured against the sample mean difference d. The null hypothesis is that Right tailedleft tailed two tailed d.f.=n – 1 n = number of pairs

Test Statistic For paired differences, the difference d of the data pairs is measured against the mean difference d. The null hypothesis is that

Test Statistic For paired differences, the difference d of the data pairs is measured against the mean difference d. The null hypothesis is that

Test Statistic For paired differences, the difference d of the data pairs is measured against the mean difference d. The null hypothesis is that The book discusses how to read the table.

Sample problem Read the handout. 1. Find all differences. 2. What are the H o and H A ? 3. Check the requirements.. paired, independent of each other randomization, histogram? 4. Find the statistics 5. Find the standard deviation and t value 6. Evaluate the P-value