1. Matched Pairs t-test Module 22a

2. Matched Pairs t-test To this point we have only looked at tests for single samples. Soon we will look at confidence intervals and hypothesis tests for comparing two groups. When each individual can be given both treatments, we can reduce the two samples to a single sample using a matched pairs design. Examples: –It can be seen in each of these examples that something pairs the two responses. –Students are each given a pre-test and a post-test to determine the amount of material learned in a given time interval. –To examine the effect of a new drug, a large group of identical twins is identified. One twin is given a treatment and the other a placebo. –A ophthalmologist is examining the importance of the dominant eye in reading. A large group of subjects is asked to read a passage with dominant eye covered and again with the non-dominant eye covered.

3. Matched Pairs t-test To analyze matched pairs data, we first reduce the data from two samples to one sample and then analyze the data using one-sample techniques. The data is reduced from two samples to one by subtracting one of the responses from the other. –We could subtract each placebo response from each treatment response. –We could subtract each pre-test score from each post-test score. –We could subtract the time taken to read the passage with the non-dominant eye from the time taken to read the passage with the dominant eye.

4. Matched Pairs t-test Example: Keyboards –“Suppose we want to compare two brands of computer keyboards, which we will denote as keyboard 1 and keyboard 2. Keyboard 1 is a standard keyboard, while keyboard 2 is specially designed so that the keys need very little pressure to make them respond. The manufacturer of keyboard 2 would like to claim that typing can be done faster using keyboard 2…A simple random sample of n = 30 teachers was selected from a population of high-school teachers attending a national conference. Each teacher typed the same page of text once using keyboard 1 and once using keyboard 2. For each teacher the order in which the keyboards were used was determined by the toss of a coin. For each teacher the variable measured was the time (in seconds) to correctly type the page of text…” (from Graybill, Iyer and Burdick, Applied Statistics, 1998).

5. Matched Pairs t-test Example: Keyboards –Information given: Sample size: n = 30.

6. Example: Keyboards 1. State the null hypothesis: 2. State the alternative hypothesis: 3. State the level of significance Matched Pairs t-test

7. Example: Keyboards 4. Calculate the test statistic. 5. Find the P-value. Remember the table gives probabilities to the right. Matched Pairs t-test

8. Example: Keyboards 6. Do we reject or fail to reject H 0 based on the P-value? 7. State the conclusion. Matched Pairs t-test