Chapter 11: The t Test Related Samples

A researcher conducts an experiment comparing two treatment conditions and obtains 20 scores in each treatment. Which design would require the smallest number of subjects?

a. a repeated-measures design

b. an independent-measures design

c. a matched-subjects design

d. either an independent-measures or a matched-subjects design

a. a repeated-measures design

For an experiment comparing two treatment conditions, an independent-measures design would obtain ____ score(s) for each subject and a repeated-measures design would obtain ____ score(s) for each subject.

a. 1, 1

b. 1, 2

c. 2, 1

d. 2, 2

b. 1, 2

For a research study comparing two treatment with n = 10 scores in each treatment, which design would require the largest number of participants?

a. repeated-measures

b. independent-measures

c. matched-subjects

d. independent-measures or match-subjects (both use the same number)

d. independent-measures or match-subjects (both use the same number

For the following data from a repeated-measures study, what is the sum of the squared deviations (SS) for the difference scores? 

I II

4 8

9 3

6 7

8 9

a. 54

b. 18

c. 12

d. 0

a. 54

For a repeated-measures hypothesis test, which of the following is the correct statement of the alternative (H₁)?

a. For the individuals in the entire population there is no consistent difference between the two treatments.

b. For the individuals in the entire population there is a consistent difference between the two treatments.

c. For the individuals in the sample there is no consistent difference between the two treatments.

d. For the individuals in the sample there is a consistent difference between the two treatments

b. For the individuals in the entire population there is a consistent difference between the two treatments

For a repeated-measures study comparing two treatment with 10 scores in each treatment, what is the df value for the t statistic?

a. 8

b. 9

c. 18

d. 19

b. 9

For a repeated-measures study comparing two treatments with a sample of n = 9 participants, a researcher obtains a sample mean difference is M_D = 5 with SS = 288 for the difference scores. What is the repeated-measures t statistic for these data?

a. 5

b. 2.5

c. 1.25

d. 0.83

b. 2.5

For a repeated-measures study comparing two treatments with n = 15 scores in each treatment, the data produce t = 1.78. If the mean difference is in the direction that is predicted by the researcher, then which of the following is the correct decision for a hypothesis test with α = .05?

a. Reject H0 for a one-tailed test but not for two-tailed.

b. Reject H0 for a two-tailed test but not for one-tailed.

c. Reject H0 for either a one-tailed test or a two-tailed test.

d. Fail to reject H0 for both a one-tailed test and a two-tailed test.

a. Reject H₀ for a one-tailed test

A repeated-measures study with 9 scores in each treatment produces a mean difference of M_D = 4.0 and SS = 288 for the difference scores. If the effect size is described using Cohen’s d, then what is the value for d?

a. 0.111

b. 0.667

c. 1.00

d. 2.00

b. 0.667

A researcher obtains a sample of n = 9 individuals and test each person in two different treatment conditions. The sample mean difference is M_D = 12 points with SS = 72. Which of the following is the correct equation for the 80% confidence interval for the population mean difference? 

a. µD = 0 ± 3(1.397)

b. µD = 0 ± 1(1.397)

c. µD = 12 ± 3(1.397)

d. µD = 12 ± 1(1.397)

d. µD = 12 ± 1(1.397)

The results of a hypothesis test with a repeated-measures t statistic are reported as follows: t(18) = 2.25, p < .05. Which of the following is consistent with the report? 

a. The study used a total of 20 participants and the mean difference was not significant.

b. The study used a total of 20 participants and the mean difference was significant.

c. The study used a total of 19 participants and the mean difference was not significant.

d. The study used a total of 19 participants and the mean difference was significant.

d. The study used a total of 19 participants and the mean difference was significant

Which of the following would have little or no influence on effect size as measured by Cohen’s d or by r²?

a. Increasing the sample size

b. Increasing the size of the sample mean difference

c. Increasing the sample variance

d. All of the other three options would influence the magnitude of effect size

a. Increasing the sample size

A researcher is using a repeated-measure study to evaluate the difference between two treatments. If there is a consistent difference between the treatments then the data should produce ____.

a. a small variance for the difference scores and a small standard error

b. a small variance for the difference scores and a large standard error

c. a large variance for the difference scores and a small standard error

d. a large variance for the difference scores and a large standard error

a. A small variance for the difference scores and a small standard error

An advantage of a repeated-measured design (compared to an independent-measures design) is that it reduces the contribution of error variability due to ____.

a. M_D

b. degrees of freedom

c. the effect of the treatment

d. individual differences

d. Individual differences

Compared to a repeated-measures design, which of the following is an advantage of an independent-measures research design?

a. It usually requires fewer participants.

b. It eliminates the concern that performance in one treatment condition may be influenced by experience in the other treatment condition.

c. It eliminates the concern that the participants in one treatment may be smarter than those in the other treatment.

d. It tends to have a smaller variance and a smaller standard error.

b. It eliminates the concern that performance in one treatment condition may be influenced by experience in the other treatment condition

For which of the following situations would be a repeated-measures design have the maximum advantage over an independent-measures design?

a. when many subjects are available and individual differences are small

b. when very few subjects are available and individual differences are small

c. when many subjects are available and individual differences are large

d. when very few subjects are available and individual differences are large

d. When very few subjects are available and individual differences are large