PSYCH 104 - Ch 10 TEST - Related-Samples t Test

What is the denominator for the estimated Cohen's d when used with the related-samples t test?

The standard deviation for the difference scores

How does computing difference scores increase the power of a related-samples t test compared to a two-independent-sample t test?

Computing difference scores eliminates between-persons error, thereby reducing the estimate for standard error in the denominator.

Distinguish between the repeated-measures design and the matched-pairs design.

Each participant is observed at least two times in the repeated-measures design. In the matched-pairs design, each pair of participants is matched and observed one time

Which of the following is a type of repeated measures design?

pre-post design within-subjects design

Which of the following is a type of repeated measures design?

both a and b

Which of the following is an assumption of the related samples t-test?

the population of difference scores is normally distributed

What are the assumptions for a related-samples t test?

Normality and independence within groups.

A researcher reports the following result for a related samples t-test at a .05 level of significance: t(40) = 3.02, p < .05 (d = .20). Is this result significant?

yes, because the p value is less than 5%

A group of 18 participants are observed two times. The critical values for a two-tailed related samples t-test at a .05 level of significance are:

±2.110

Using the same data as in Question 3, what is the proportion of variance explained using omega-squared? Is this a small, medium, or large effect size?

ω2 = 2.4^2 - 1 /2,4^2+ 20 = 0.18 (medium effect size)

How do related samples differ from independent samples?

In related samples, participants are related because they are either observed more than once or matched on common traits. In independent samples, participants are not related because different participants are observed in each group

Computing difference scores prior to computing the test statistic reduces error by eliminating one possible source of error, thereby increasing the power of a hypothesis test.

True

What value is placed in the denominator of the test statistic for the related-samples t test?

Estimated standard error for difference scores

Using a repeated measures design, Researcher A computes the following test statistic, t(22) = 1.980, and decides to reject the null hypothesis. Using a matched samples design, Researcher B computes the same test statistic, t(22) = 1.980, but decides to retain the null hypothesis. Which of the follow can explain why this occurred?

Researcher A computed a one-tailed test; Researcher B computed a two-tailed test

What is the value for the degrees of freedom for each example listed below? a) A study comparing 10 matched pairs of scores b) A study involving 18 participants observed two times

a) df = 9, b) df = 17

What value is placed in the denominator of the formula for estimated Cohen's d for the related samples t-test?

the standard deviation of the difference scores

Scores that are obtained by subtracting paired scores for two related samples are called:

difference scores

A researcher wants to study differences in mood after listening to music. Before conducting the study, the researcher has participants report how often they listen to music (in minutes) per week. Participants are matched based on their responses, and differences in mood between matched pairs of participants are computed. What type of strategy was used to match participants?

matching through experimental manipulation

A psychologist reports that the value of the test statistic for two related samples is 2.400. If the degrees of freedom are 20, then what is the value for eta-squared? Is this a small, medium, or large effect size?

η2 = 2.4^2/2,4^2+ 20 = 0.22 (medium effect size)

A researcher records the amount of computer use (in hours per day) in a sample of students and then matches the students based on their amount of computer use. Is this an example of matching through experimental manipulation or matching through natural occurrence?

Matching through experimental manipulation.

The related-samples t test can be used for the repeated-measures design and the matched-pairs design.

True

The test statistic for a related-samples t test is + 2.100. Using a .05 level of significance, would you retain or reject the null hypothesis under each of the following conditions? a) df = 10, two-tailed test b) df = 30, one-tailed test (upper tail critical) c) df = 20, two-tailed test d) df = 40, one-tailed test (lower tail critical)

a) Retain the null hypothesis b) Reject the null hypothesis c) Reject the null hypothesis d) Retain the null hypothesis

A researcher conducts a study with 16 pairs of students matched based on their SAT scores. In this study, he measures a mean difference in reading comprehension equal to 5 (MD = 5). The null hypothesis states that the mean difference is zero. What is the value of the test statistic for a related-samples t test if the estimated standard error for difference scores is equal to each of the following? a) 4 b) 8 c) 15

a) t obt = 5/4 = 1.250 b) t obt = 5/8 = 0.625 c) t obt = 5/15 = 0.333

An advantage of computing difference scores in the related samples t-test is that it:

reduces variability reduces standard error increases power

A statistical procedure used to test hypotheses concerning two related samples selected from populations in which the variance in one or both populations is unknown is called:

related samples t-test

The mean difference between two related samples is 4.00. What is the value for an estimated Cohen's d if a sample standard deviation for the difference scores in this example is equal to (a) 4 and (b) 40?

(a) d = 4/4 = 1.00 b) d = 4/40 = 0.10

A researcher computes the following test statistic for a related samples t-test: t(22) = 3.14, p < .05. What is the proportion of variance for this test using the formula for omega-squared?

0.28

A group of 20 participants are observed two times. The related samples t-test for this study will have a degrees of freedom equal to:

19

Why do we find the difference between pairs of scores (compute difference scores) before computing the test statistic for a related-samples t test?

Computing difference scores eliminates the between-persons error, thereby increasing the power of the test

Name two types of repeated-measures designs.

Pre-post design and within-subjects design

What is the test statistic for a related-samples t test with a mean difference equal to 5 and an estimated standard error for difference scores equal to each of the following? a) 2.5 b) 5.0 c) 10.0

a) t obt = 5/2.5 = 2.00 b) t obt = 5/5 = 1.00 c) t obt = 5/10 = 0.50

How does selecting related samples minimize the estimate for standard error?

it allows us to compute difference scores prior to computing the test statistic it eliminates the between-persons source of error

Three advantages for selecting related samples include each of the following, except:

it decreases the likelihood of a Type I error