Psych 295 Test 3

A repeated-measures research study uses a total of 20 participants to compare two treatment conditions. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.729.

True

For a one-tailed test with a = .05 and a sample of n = 9, the critical value for the t statistic is t = 1.860.

True

The t distribution for df = 4 is flatter and more spread out than the t distribution for df = 20.

True

A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?

d = 0.50

A sample of difference scores has a mean of MD = 5 with a variance of s2 = 100. If effect size is measured using Cohen's d, what is the value of d?

d = 5/10

A sample of n = 4 scores is selected from a population with an unknown mean. The sample has a mean of M = 40 and a variance of s2 = 16. Which of the following is the correct 90% confidence interval for μ?

μ = 40 ± 2.353(2)

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18. If the two samples are the same size, how many participants were in each of the samples?

10

A repeated-measures study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study?

11 for repeated-measures and 12 for independent-measures

One sample has n = 5 scores and the second has n = 10 scores. If the pooled variance for the two samples is 30, what is the value of the estimated standard error for the sample mean difference?

3

Two samples, each with n = 9 scores, produce an independent-measures t statistic of t = 2.00. If the effect size is measured using r2, what is the value of r2?

4/20

If two separate samples have M1 = 10 and M2 = 18 with a pooled variance of 16, then Cohen's d = 0.50.

False

Which of the following would have no effect on the width of a confidence interval?

Increase the sample mean

In general, if the variance of the difference scores increases, what will happen to the value of the t statistic?

It will decrease (move toward 0 at the center of the distribution).

If other factors are held constant, what is the effect of increasing the sample variance?

It will increase the estimated standard error and increase the likelihood of rejecting H0.

A researcher reports an independent-measures t statistic with df = 16. How many participants were in the entire study?

18

A researcher obtains t(20) = 2.00 and MD = 9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?

4/24

A research report describing the results from a repeated-measures t test states that: t(22) = 1.71, p > .05. From this report, what was the outcome of the hypothesis test?

Fail to reject the null hypothesis with a sample of n = 23 participants

A research study compares the mean weight for a sample of n = 36 participants before they begin a 6-week diet and their mean weight at the end of the diet. This is an example of an independent-measures design.

False

An independent-measures study with n = 20 scores in each treatment will produce an independent-measures t statistic with df = 19.

False

If an independent-measures t statistic has df = 20, then there were a total of 18 individuals participating in the research study.

False

How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?

Larger variance increases the standard error but decreases measures of effect size.

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that μ = 80?

M = 90 and small sample variance

Which of the following describes the effect of increasing sample size?

There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.

For an independent-measures t statistic, you typically must compute the pooled variance before calculating the estimated standard error.

True

If a set of n = 9 difference scores has a mean of MD = 3.5 and a variance of s2 = 36, then the sample will produce a repeated-measures t statistic of t = 3.5/2.

True

The following data are from an independent-measures experiment comparing two treatment conditions: Treatment 1 Treatment 2 6 19 13 9 8 18 4 10 13 12 4 14 11 19 5 11 a. Do these data indicate a significant difference between the treatments at the .05 level of significance? b. Compute r2 to measure the size of the treatment effect. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

a. For treatment 1, M = 8 and SS = 104. For treatment 2, M = 14 and SS = 120. The pooled variance is 16, the standard error is 2, and t(14) = 3.00. Reject H0. b. For these data, r2 = 9/23 = 0.391. c. The data indicate a significant difference between treatments, t(14) = 3.00, p < .05, r2 = 0.391.

For the following data from a repeated-measures study: Subject Treatment 1 Treatment 2 A 12 14 B 6 16 C 8 10 C 9 12 a. Find the difference scores b. Calculate MD and the variance for the difference scores c. Calculate the estimated standard error for the mean difference

a. The difference scores are 2, 10, 2, 3 b. MD = 4.25 and s2 = 14.92 c. The standard error is 1.93.

A sample is selected from a population with μ = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s2 = 64. a. If the sample has n = 4 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen's d to measure the size of the treatment effect. Use a two-tailed test with a = .05. b. If the sample has n = 16 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen's d to measure the size of the treatment effect. Use a two-tailed test with a = .05. c. Describe how increasing the size of the sample affects the likelihood of rejecting the null hypothesis and the measure of effect size.

a. The standard error is 4 and t = 1.25.With df = 3, the critical value is t = 3.182. Fail to reject the null hypothesis. Cohen's d = 5/8 = 0.625. b. The standard error is 2 and t = 2.50. With df = 15, the critical value is t = 2.131. Reject the null hypothesis. Cohen's d = 5/8 = 0.625. c. Increasing sample size increases the likelihood of rejecting the null hypothesis but has little or no effect on measures of effect size.

Compared to an independent-measures design, a repeated-measured study is more likely to find a significant effect because it reduces the contribution of variance due to ______.

individual differences

A sample is selected from a population with μ = 70, and a treatment is administered to the sample. After treatment, the sample mean is M = 74, and Cohen's d is d = 1.00. What is the value of the sample variance?

s2 = 16