Question

In the following examples, indicate whether you would perform a t-test of independent samples or dependent samples.

a. Two groups were exposed to different levels of treatment for ankle sprains. Which treatment was more effective?
b. A group of adolescent boys was offered interpersonal skills counseling. They were then tested in September and May to see if there was any impact on family harmony.
c. One group of adult men was given instructions for reducing their high blood pressure, whereas another group was not given any instructions. The blood pressure of men in both groups was measured before and after.
d. One group of men was provided access to an exercise program and tested two times over a 6-months period for heart health

Answer 1

An independent samples t-test is used for comparing means from two unrelated groups. A matched pairs t-test is used for comparing related samples or the same group under different conditions. In the provided math textbook example, a matched pairs t-test is appropriate.

Step-by-step explanation:

Independent Samples vs. Matched Pairs T-Test

When comparing two means from different groups, researchers use either an independent samples t-test or a matched pairs (also called dependent samples) t-test. The choice between the two depends on the design of the study and the relationship between the samples.

Independent Samples T-Test

This test compares the means from two groups that are unrelated. Each group represents a different population or a different treatment condition.

Matched Pairs T-Test

This test is used when comparing two related samples or the same group under different conditions or time points.

Regarding the example you provided about investigating the effectiveness of a new math textbook for high school students, the groups are matched because you are examining the same students at different times (beginning and end of the semester). Hence, a matched pairs t-test would be used to compare the pretest and posttest scores.

For scenario 118, if a = 0.05 and the p-value is 0.0014, the conclusion would be that there is sufficient evidence to conclude that the blood pressure decreased after the training, because the p-value is less than the significance level (alpha). This scenario seems to imply the use of a dependent means test, likely a matched pairs t-test if the same individuals' blood pressures were measured before and after training.

In the case of the powder diet vs. liquid diet study (scenario 123), since the two groups are different and received different treatments, an independent samples t-test would be used, likely option B as the population standard deviations are unknown.