Problem Set Week 7 Chapter 11

Answer: Steps completed to determine the answer should also be included.

2.) Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause problems. Briefly explain how these problems are eliminated or reduced with a repeated-measures study.

10.) Research has shown that losing even on nights sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this phenomenon, a sample of college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged MD.7 points better on the first test with a variance of s^ for the difference scores.

A) Do the data indicated a significant change in problem solving ability? Use a two-tailed test with =.05

B) Compute an estimated cohens d to measure the size of the effect.

12.) How would you react to doing much worse on an exam than you expected? There is some evidence to suggest that most individuals believe that they can cope with this kind of problem better than their fellow students (Igou, 2008). In the study, participants read a scenario of a negative event and were asked to use a 10-point scale to rate how it would affect their immediate well-being (-5 strongly worsen to +5 strongly improve). Then they were asked to imagine the event from the perspective of an ordinary fellow student and rate how it would affect that person. The difference between the two ratings was recorded. Suppose that a sample of participants produced a mean difference of MD.28 points (self rated higher) with a standard deviation of .50 for the difference scores.

A) Is this result sufficient to conclude that there is a significant difference in the ratings for self versus others? Use a two-tailed test with =.05

B) Compute r^2 and estimate Cohens d to measure the size of the treatment effect.

C) Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

16.) A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participants ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the participants began a second 30-day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 20-day period, cholesterol levels were measured again and the researcher recorded the difference between the two scores for each participant. For this sample, cholesterol scores averaged points lower with the oatmeal diet with for the difference scores.

A) Is the data sufficient to indicate a significant change in cholesterol level? Use a two-tailed test with =.01

B) Compute r^2, the percentage of variance accounted for by the treatment, to measure the size of the treatment effect.

C) Write a sentence describing the outcome the hypothesis test and the measure of effect size as it would appear in a research report.

18.) One of the primary advantages of a repeated-measures design, compared to independent-measures, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing two treatment conditions.

A) Assume that the data are from an independent measures study using two separate samples, each with participants. Compute the pooled variance and the estimated standard error for the mean difference.

B) Now assume that the data are from a repeated measures study using the same sample of participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (You should find that the repeated measures design substantially reduces the variance and the standard error.)

Treatment 1 Treatment 2 Treatment 3

10 13 3

12 12 0

8 10 2

6 10 4

5 6 1

7 9 2

M = 8 M = 10 MD = 2

SS = 34 SS = 30 SS = 10

20.) A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a group of 20- to 29-year-old non-pet owners and a similar age group of pet owners. The pet owners are matched one to one with the non-pet owners for income, number of close friendships, and general health. The data are as follows:

Matched Pair Non-Pet Owner Pet Owner

A 12 14

B 8 7

C 10 13

D 9 9

E 7 13

F 10 12

A) Is there a significant difference in the mood scores for non-pet owners versus pet owners? Test with =.05 for two tails.

B) Construct the 95% confidence interval to estimate the size of the mean difference in mood between the population of pet owners and the population of non-pet owners. (You should find that a mean difference of D is an acceptable value, which is consistent with the conclusion from the hypothesis test.)

Final question:

1.) Write the null and alternative hypotheses for the following items 10, 12, 16, 18, and 20.