Question 1

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 2

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 likelihood of rejecting the null hypothesis because it would make it more likely that the observed difference between the sample means is due to a real difference between the population means, rather than due to chance.

Question 3

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 ______. A)M_D B)degrees of freedom C)the effect of the treatment D)individual differences

Accepted Answer

A repeated-measures design involves using the same participants in all conditions, which reduces the influence of individual differences on the results. Therefore, it is more likely to find a significant effect as it eliminates this source of variance.

Question 4

A research report describing the results from a repeated-measures t test states, "t(22) = 1.71, p > .05." From this report you can conclude that the outcome of the hypothesis test was ______.
A)to reject the null hypothesis with a sample of n = 23 participants
B)to fail to reject the null hypothesis with a sample of n = 23 participants
C)to reject the null hypothesis with a sample of n = 22 participants
D)to fail to reject the null hypothesis with a sample of n = 22 participants

Accepted Answer

The report indicates that the p-value is greater than .05, which means the null hypothesis was not rejected. The degrees of freedom (22) suggest a sample size of 23 participants.

Question 5

A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop.Each student's grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop.The average GPA improved by M_D = 0.60 points with s² = 0.09.The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population.Which of the following is the 80% confidence interval for these data? A)µ_D = 0.60 + 0.01(1.397) B)µ_D = 0.60 + 0.09(1.860) C)µ_D = 0.60 + 0.10(1.397) D)µ_D = 0.60 + 0.10(1.860)

Accepted Answer

The answer of A sample of n = 9 college...

Question 6

In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition.One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment.This problem is called ______.
A)individual differences
B)order effects
C)homogeneity of variance
D)bi-treatment effect

Accepted Answer

Order effects refer to the influence that the sequence of treatments can have on the participants' responses, which is a concern in repeated-measures designs.

Question 7

For a research study comparing two treatment conditions, a repeated-measures design would require two scores for each participant but an independent-measures design would require only one score for each participant.

Accepted Answer

In a repeated-measures design, the same participants are measured under both conditions, resulting in two scores per participant. In an independent-measures design, different participants are used for each condition, so each participant provides only one score.

Question 8

Which of the following possibilities is a serious concern with a repeated-measures study?
A)You will obtain negative values for the difference scores.
B)The results will be influenced by order effects.
C)The mean difference is due to individual differences rather than treatment differences.
D)All of the other options are major concerns.

Accepted Answer

Order effects occur when the order in which the treatments are given affects the outcome. For example, a participant may perform better on a task during the second session simply because they have already done it before in the first session. This can impact the validity of the study and interpretation of the results. Therefore, it is important to counterbalance the order of treatments to minimize any potential order effects. The other options (A and C) are still important considerations in a repeated-measures study, but they may not necessarily be serious concerns depending on the specific study design and research question.

Question 9

What value is estimated with a confidence interval using the repeated-measures t statistic?
A)the mean for a sample of difference scores
B)the mean for a population of difference scores
C)the difference between two population means
D)the difference between two sample means

Accepted Answer

A confidence interval using the repeated-measures t statistic is used to estimate the mean for a population of difference scores, not just a sample. This approach is typically used in within-subjects designs where the same subjects are measured under different conditions, and the interest is in estimating the mean difference in scores across these conditions for the entire population from which the sample was drawn.

Question 10

A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment.If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find ______.
A)a sample mean difference near zero
B)a t statistic 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 a consistent improvement of 8 or 9 points, the variance of the difference scores will be near zero because there is little variability in the scores.

Question 11

A researcher obtains t = 2.35 for a repeated-measures study using a sample of n = 8 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 either α = .05 or α = .01
C)fail to reject the null hypothesis with either α = .05 or α = .01
D)cannot make a decision without additional information

Accepted Answer

The answer of A researcher obtains t = 2.35 for...

Question 12

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 of the sample of difference scores leads to an increase in the standard error because the standard error is directly proportional to the square root of the variance. As the standard error increases, the precision of the estimate decreases, causing a decrease in the value of t. Therefore, an increase in variance leads to a decrease in the value of t.

Question 13

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 the significance level suggest that the results are statistically significant. The degrees of freedom indicate that the sample size is relatively small. The formula for degrees of freedom in a repeated-measures t-test is df = n-1, where n is the number of participants. Therefore, 12 = n - 1, which means that n = 13. Therefore, the correct answer is B.

Question 14

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 larger number of scores typically increases the power of the test, but a smaller variance is more likely to produce significant results because it indicates a stronger effect size. A smaller variance means that the scores are more tightly clustered around a central value, which makes it easier to detect differences between the two conditions being compared.

Question 15

If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study? A)M_D = 5 with s² = 5 for the difference scores B)M_D = 5 with s² = 10 for the difference scores C)M_D = 3 with s² = 10 for the difference scores D)M_D = 3 with s² = 20 for the difference scores

Accepted Answer

The confidence interval for the difference in means is calculated as (point estimate) ± t(df, α/2) * (standard error of the difference), where - the point estimate is the sample mean difference - t(df, α/2) is the critical value from the t-distribution, with df degrees of freedom and α/2 significance level (for a 90% confidence interval, α = 0.1 and α/2 = 0.05) - the standard error of the difference is calculated as s / sqrt(n), where s is the sample standard deviation of the difference scores, and n is the sample size To produce the widest confidence interval for the population mean difference, we want the standard error of the difference to be as large as possible, while keeping the sample size constant. Therefore, we want the sample standard deviation of the difference scores to be as large as possible, given the same sample size. Choice D has the largest s² value (20), so it will produce the widest confidence interval.

Question 16

In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic?
A)It will increase (move farther toward the tail of the distribution).
B)It will decrease (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 relies on the standard error of the difference scores, which is affected by the variance of the difference scores. As variance increases, the standard error also increases, which causes the t statistic to decrease (move toward 0 at the center of the distribution).

Question 17

For which of the following situations would 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

Accepted Answer

A repeated-measures design is most advantageous when there are few subjects and large individual differences, as it controls for variability between subjects by using the same subjects in all conditions.

Question 18

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 in difference scores suggests that the treatment effect is not consistent across the sample, leading to a lower likelihood of identifying a significant difference due to the increased variability.

Question 19

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

If the difference between the treatments is consistent from one participant to another, then the difference scores will have low variability (small variance) and the standard error will also be small. This is because there is less variability in the data, making it more precise and reliable.

Question 20

A research report describing the results from a repeated-measures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05.Based on this report, you can conclude that a total of ____ 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 the number of subjects minus one (N-1). The report mentions t(10), indicating the degrees of freedom are 10, which means there were 11 participants (since 10 + 1 = 11).

Quiz 11: The T Test for Two Related Samples

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?

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

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 ______.

A research report describing the results from a repeated-measures t test states, "t(22) = 1.71, p > .05." From this report you can conclude that the outcome of the hypothesis test was ______.

For a research study comparing two treatment conditions, a repeated-measures design would require two scores for each participant but an independent-measures design would require only one score for each participant.

Which of the following possibilities is a serious concern with a repeated-measures study?

What value is estimated with a confidence interval using the repeated-measures t statistic?

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

A researcher obtains t = 2.35 for a repeated-measures study using a sample of n = 8 participants.Based on this t value, what is the correct decision for a two-tailed test?

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

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

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

If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?

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

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

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

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 research report describing the results from a repeated-measures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05.Based on this report, you can conclude that a total of ____ individuals participated in the research study .