Statistics module 15 - t Test for Two Related Samples

Question

Exercise 5

Each of the following studies requires a t test for one or more population means. Specify whether the appropriate t test is for one sample, two independent samples, or two related samples, and in the latter case, whether it involves repeated measures or matched pairs of different subjects. 

 

1. College women who are being treated for depression at the campus counseling center were matched for initial depression and then assigned to a drug treatment condition or a placebo control condition. At the end of the treatment period, the women take a depression test and their test scores are analyzed. 
2. Children who have poor social skills are selected to participate in social skills training. The researcher observes the children on the playground both before and after the social skills training. For each child, she records the number of positive peer interactions. She then analyzes the mean before-after difference. 
3. A researcher randomly assigns high school seniors to either an experimental group where they learn about time management or to a control group where they discuss current events. The researcher then gathers information, for all students, on homework completion. The researcher wants to find out if the time management session is effective for improving homework completion among high school seniors. 
4. A researcher reads that the average time that adults in the United States spend watching TV is 28 hours per week. The researcher randomly selects a sample of college students. The researcher wants to find out if college students also watch TV an average of 28 hours per week. 
5. A Japanese educational researcher reads that American elementary students spend an average of 21 minutes each weekday doing homework. The researcher records the time spent on homework for a sample of Japanese elementary students. The researcher wants to find out if Japanese students study more than 21 minutes each weekday.

Answer 1

1. The appropriate statistic in this situation would be the related samples t-test because this is a matched samples design. It is a matched samples design because the women in each treatment condition were initially matched based on initial depression score.
2. The appropriate statistic in this situation would be the related samples t-test because this is a repeated measures design. It is a repeated measures design because we are comparing the same children under multiple periods of observation (before and after).
3. The appropriate statistic in this situation would be the independent samples t-test because this is a between-subjects design. It is a between-subjects design because we are comparing two independent groups (i.e., there is no reason to choose one specific person from each condition and compare them, this is a difference between groups not individuals).
4. The appropriate statistic in this situation would be the one sample t-test because this is comparing a sample with a known population. This test would be two-tailed because the question does not specify a direction of difference.
5. The appropriate statistic in this situation would be the one sample t-test because this is comparing a sample with a known population. This test would be one-tailed because the question does specify a direction of difference (e.g., more than 21 minutes each weekday).