Question 1

A researcher is using a repeated-measures study to evaluate the difference between two treatments.If the difference between the treatments is consistent from one participant to another,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

Accepted Answer

A small variance for the difference scores would indicate that the difference between the treatments is consistent across participants. A small standard error would further indicate that the sample mean is a good estimate of the population mean, which is desirable in research. Therefore, a small variance for the difference scores and a small standard error would be optimal in this scenario.

Question 2

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces MD = 3 with SS = 48 for the set of difference scores.What is the repeated-measures t statistic for these data?
A)3/√3 = 1.73
B)3/2 = 1.50
C)3/4 = 0.75
D)3/16 = 0.19

Accepted Answer

The repeated-measures t statistic formula is t = MD / (SDdiff / sqrt(n)). Since n = 4 and SS = 48, then the variance of the difference scores is: SS / (n-1) = 48 / 3 = 16. Thus, the standard deviation of the difference scores is sqrt(16) = 4. Plugging in the values, we get t = 3 / (4 / sqrt(4)) = 3 / 2 = 1.5. Therefore, the correct answer is B.

Question 3

In general,what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?
A)A large number of scores and a large variance
B)A large number of scores and a small variance
C)A small number of scores and a large variance
D)A small number of scores and a small variance

Accepted Answer

A large number of scores increases the power of the test, whereas a small variance makes the differences between the scores more pronounced, making it easier to detect significant differences. Therefore, a large number of scores and a small variance are most likely to produce a significant t statistic for the repeated-measures hypothesis test.

Question 4

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?
A)5/10
B)5/100
C)25/100
D)Cannot determine without knowing the sample size

Accepted Answer

Cohen's d is calculated as the mean difference (MD) divided by the standard deviation (s). The standard deviation is the square root of the variance, so s = sqrt(100) = 10. Therefore, d = 5 / 10.

Question 5

For a repeated-measures study comparing two treatment conditions,a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s² = 36.What is the value for the repeated-measures t statistic for these data?
A)4/2
B)4/4
C)4/6
D)4/36

Accepted Answer

The repeated-measures t statistic is calculated as the mean difference divided by the standard error of the mean difference. The standard error of the mean difference is calculated as the square root of the variance divided by the sample size. Therefore, the repeated-measures t statistic for these data is 4 / (sqrt(36/9)) = 4 / 2 = 2.

Question 6

A researcher obtains t = 2.25 for a repeated-measures study using a sample of n = 10 participants.Based on this t value,what is the correct decision for a two-tailed test?
A)Reject the null hypothesis with α = .05 but not with α = .01
B)Reject the null hypothesis with both α = .05 and α = .01
C)Fail to reject the null hypothesis with both α = .05 and α = .01
D)Cannot make a decision without additional information

Accepted Answer

The answer of A researcher obtains t = 2.25 for...

Question 7

A researcher reports t(12)= 2.86,p < .05 for a repeated-measures research study.How many individuals participated in the study?
A)n = 11
B)n = 13
C)n = 24
D)n = 25

Accepted Answer

The t-value and significance level indicate that there was a significant difference between the two conditions in this repeated-measures study. The degrees of freedom can be calculated as n-1, where n is the number of participants. Using a t-table, we can find that the critical value for t with 11 degrees of freedom at p < .05 is 2.201. Since the obtained t-value (2.86) is greater than the critical value, we can conclude that the results are statistically significant. Therefore, the number of participants in the study would be 13 (n = 12 + 1).

Question 8

In general,if the variance of the difference scores increases,what will happen to the value of the t statistic?
A)It will increase in magnitude (move farther toward the tail of the distribution).
B)It will decrease in magnitude (move toward 0 at the center of the distribution).
C)It will stay the same; the t statistic is not affected by the variance of the difference scores.
D)It may increase or may decrease; there is no consistent relationship between variance and the size of the t statistic.

Accepted Answer

The t statistic is inversely related to the standard deviation (or square root of the variance) of the difference scores. As the variance of the difference scores increases, the denominator of the t formula (which includes the standard deviation of the differences) increases, leading to a smaller t value, or a decrease in magnitude.

Question 9

In general,what is the effect of an increase in the variance for the sample of difference scores?
A)An increase in the standard error and an increase in the value of t
B)An increase in the standard error and a decrease in the value of t
C)A decrease in the standard error and an increase in the value of t
D)A decrease in the standard error and a decrease in the value of t

Accepted Answer

An increase in the variance for the sample of difference scores will increase the standard error because a larger variance indicates that the sample means are more spread out and less likely to represent the population mean. This greater variability means that the t-value will decrease because it becomes less likely that the observed difference is significant. Therefore, the correct answer is B: An increase in the standard error and a decrease in the value of t.

Question 10

A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments,t(10)= 1.65,p > .05.Based on this report,how many individuals participated in the research study?
A)9
B)10
C)11
D)12

Accepted Answer

In a repeated-measures study, the degrees of freedom (df) for a t-test are calculated as n - 1, where n is the number of participants. Given that df = 10, we solve for n: n - 1 = 10, thus n = 11.

Question 11

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94.The treatment is expected to increase scores and the sample mean shows an increase.Which of the following is the correct decision for a hypothesis test using α = .05?
A)Reject the null hypothesis with a one-tailed test but fail to reject with two tails
B)Reject the null hypothesis with either a one-tailed or a two-tailed test
C)Fail to reject the null hypothesis with either a one-tailed or a two-tailed test
D)Fail to reject the null hypothesis with a one-tailed test but reject with two tails

Accepted Answer

A t of 1.94 for a sample of 16 participants is significant at α = .05 with a one-tailed test, but not with a two-tailed test. Since the researcher had an a priori hypothesis that the treatment would increase scores, a one-tailed test would be appropriate. Therefore, the null hypothesis should be rejected with a one-tailed test but fail to reject with a two-tailed test.

Question 12

If a repeated-measures study shows a significant difference between two treatments with α = .01,then what can you conclude about measures of effect size?
A)The value of Cohen's d is large.
B)The percentage of variance explained (r²) is large.
C)Both Cohen's d and r² are large.
D)A significant effect does not necessarily mean that the effect size will be large.

Accepted Answer

A significant effect only indicates that there is a difference between the two treatments, but it does not provide any information about the magnitude of the difference or the effect size. Therefore, we cannot conclude anything about measures of effect size based solely on the fact that there is a significant difference between the treatments. Option A and B suggest that the effect size is large, which is not necessarily true based on statistical significance alone. Option C suggests that both measures of effect size are large, but this is not a necessary conclusion based on statistical significance alone.

Question 13

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?
A)n = 15 and MD = 2
B)n = 15 and MD = 4
C)n = 30 and MD = 2
D)n = 30 and MD = 4

Accepted Answer

The repeated-measures t test compares the means of two related groups on the same variable, and is used to test whether the differences between the two means are statistically significant. The t statistic takes into account the magnitude of the difference between the two means, as well as the size of the sample and the variability within each group. Therefore, a larger sample size (n = 30) and a larger difference between the means (MD = 4) are more likely to produce a significant t statistic compared to the other options with smaller sample sizes or smaller differences between the means. Therefore, D is the best choice.

Question 14

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?
A)9/20
B)9/29
C)4/13
D)4/24

Accepted Answer

The effect size r² for a repeated-measures study can be calculated using the formula r² = t² / (t² + df), where t is the t-value and df is the degrees of freedom. Here, t = 2.00 and df = 20, so r² = 2² / (2² + 20) = 4 / (4 + 20) = 4/24.

Question 15

For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s² = 16.What is the value of the sample mean?
A)MD = 2
B)MD = 4
C)MD = 8
D)MD = 16

Accepted Answer

Cohen's d is calculated as the mean difference (MD) divided by the standard deviation (s). Given Cohen's d = 0.50 and the variance s² = 16 (thus, s = 4), we can solve for MD: MD = d * s = 0.50 * 4 = 2.

Question 16

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?
A)n = 15 and SS = 10 for the difference scores
B)n = 15 and SS = 100 for the difference scores
C)n = 30 and SS = 10 for the difference scores
D)n = 30 and SS = 100 for the difference scores

Accepted Answer

The repeated-measures t statistic is more likely to be significant with a larger sample size (n) and a smaller sum of squares (SS) for the difference scores, as this suggests less variability and more reliability in the differences measured. Therefore, option C (n = 30 and SS = 10) is most likely to produce a significant value because it combines a relatively large sample size with low variability in the difference scores.

Question 17

What is indicated by a large variance for a sample of difference scores?
A)A consistent treatment effect and a high likelihood of a significant difference
B)A consistent treatment effect and a low likelihood of a significant difference
C)An inconsistent treatment effect and a high likelihood of a significant difference
D)An inconsistent treatment effect and a low likelihood of a significant difference

Accepted Answer

A large variance for a sample of difference scores indicates an inconsistent treatment effect, meaning the scores are spread out and not consistent. This lowers the likelihood of a significant difference because the scores are not consistently different from one another.

Question 18

Assuming that other factors are held constant,which of the following would tend to increase the likelihood of rejecting the null hypothesis?
A)Decrease the sample size
B)Increase the sample mean difference
C)Increase the sample variance
D)None of the other 3 options would increase the likelihood.

Accepted Answer

Increasing the sample mean difference would increase the distance between the sample mean and the null hypothesis value, making it more likely for the null hypothesis to be rejected. Decreasing the sample size or increasing the sample variance would make it more difficult to reject the null hypothesis. Therefore, option A and C are incorrect, and option D is incorrect because option B would increase the likelihood of rejecting the null hypothesis.

Question 19

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all the participants show improved performance of 8 or 9 points after treatment,what should the researcher find?
A)The sample mean difference is near zero.
B)The t statistic is near zero.
C)The variance of the difference scores is near zero.
D)None of the other options is correct.

Accepted Answer

If all participants show the same improvement, the variance of the difference scores will be very low, approaching zero. This is because there are no individual differences to account for in the change scores, so the differences will be very consistent. Therefore, the researcher should find that the variance of the difference scores is near zero. The sample mean difference will also be 8 or 9 points, but this does not necessarily mean that the mean is near zero, as the starting point could have been much lower or higher. The t statistic will depend on the sample size and standard deviation, so it is not necessarily near zero either.

Question 20

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?
A)Reject the null hypothesis with a sample of n = 23 participants
B)Fail to reject the null hypothesis with a sample of n = 23 participants
C)Reject the null hypothesis with a sample of n = 22 participants
D)Fail to reject the null hypothesis with a sample of n = 22 participants

Accepted Answer

The outcome of the hypothesis test indicates that the p-value is greater than .05, which typically means there is not enough evidence to reject the null hypothesis. The degrees of freedom (df) for a repeated-measures t-test is n - 1, where n is the sample size. Given t(22), the sample size is 23 (since 22 + 1 = 23), leading to the conclusion to fail to reject the null hypothesis with a sample of n = 23 participants.

Quiz 11: The t Test for Two Related Samples

A researcher is using a repeated-measures study to evaluate the difference between two treatments.If the difference between the treatments is consistent from one participant to another,then the data should produce ______.

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces MD = 3 with SS = 48 for the set of difference scores.What is the repeated-measures t statistic for these data?

In general,what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?

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?

For a repeated-measures study comparing two treatment conditions,a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s² = 36.What is the value for the repeated-measures t statistic for these data?

A researcher obtains t = 2.25 for a repeated-measures study using a sample of n = 10 participants.Based on this t value,what is the correct decision for a two-tailed test?

A researcher reports t(12) = 2.86,p < .05 for a repeated-measures research study.How many individuals participated in the study?

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

In general,what is the effect of an increase in the variance for the sample of difference scores?

A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments,t(10) = 1.65,p > .05.Based on this report,how many individuals participated in the research study?

If a repeated-measures study shows a significant difference between two treatments with α = .01,then what can you conclude about measures of effect size?

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

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?

For a repeated-measures study comparing two treatment conditions,a researcher obtains Cohen's d = 0.50 for a sample of n = 4 scores with a variance of s² = 16.What is the value of the sample mean?

If other factors are held constant,which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

What is indicated by a large variance for a sample of difference scores?

Assuming that other factors are held constant,which of the following would tend to increase the likelihood of rejecting the null hypothesis?

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all the participants show improved performance of 8 or 9 points after treatment,what should the researcher find?

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?