10.3 STATISTICAL INFERENCES FOR TWO RELATED POPULATIONS

In the preceding section, hypotheses were tested and confidence intervals constructed about the difference in two population means when the samples are independent. In this section, a method is presented to analyze dependent samples or related samples. Some researchers refer to this test as the matched-pairs test. Others call it the t test for related measures or the correlated t test.

What are some types of situations in which the two samples being studied are related or dependent? Let's begin with the before-and-after study. Sometimes as an experimental control mechanism, the same person or object is measured both before and after a treatment. Certainly, the after measurement is not independent of the before measurement because the measurements are taken on the same person or object in both cases. Table 10.4 gives data from a hypothetical study in which people were asked to rate a company before and after one week of viewing a 15-minute DVD of the company twice a day. The before scores are one sample and the after scores are a second sample, but each pair of scores is related because the two measurements apply to the same person. The before scores and the after scores are not likely to vary from each other as much as scores gathered from independent samples because individuals bring their biases about businesses and the company to the study. These individual biases affect both the before scores and the after scores in the same way because each pair of scores is measured on the same person.