Question 1

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces a mean of M = 18 with SS = 24 for the scores in the first treatment,a mean of M = 14 with SS = 18 for the scores in the second treatment,and a mean of M_D = 4 with SS = 12 for the difference scores.What is the estimated standard error for the sample mean difference?

Accepted Answer

D

Question 2

A repeated-measures study uses a total of n = 10 participants to compare two treatment conditions.How many scores are measured in this study,and how many scores are actually used to compute the sample mean and the sample variance?

Accepted Answer

A

Question 3

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

Accepted Answer

Cohen's d is calculated as the mean difference divided by the standard deviation. Here, the standard deviation is the square root of the variance, which is 10. Therefore, d = 5/10 = 0.5.

Question 4

For a repeated-measures study,if the null hypothesis is true,then what value should be obtained for the sample mean.

Accepted Answer

If the null hypothesis is true in a repeated-measures study, the sample mean difference between the two conditions should be close to 0. Therefore, the best choice is D, which indicates that M_D is near 0.

Question 5

Which of the following is the correct null hypothesis for a repeated-measures t test?

Accepted Answer

The correct null hypothesis for a repeated-measures t test involves testing the difference between the means of two related samples (in this case, two measurements taken from the same group of participants) and determining if it is statistically significant. Therefore, the correct notation for the null hypothesis would involve the symbol for the population mean (µ) rather than the symbol for the variance (MS) or a comparison between different levels of the independent variable (B1 and B0). Option B provides the correct notation for the null hypothesis, stating that the population mean of the difference scores between two measurements is equal to 0.

Question 6

The null hypothesis for a repeated-measures test states,

Accepted Answer

The null hypothesis for a repeated-measures test states that the entire population will have a mean difference of μ_D = 0. Option A refers to each individual having a difference score of zero, which is not the correct wording for the null hypothesis. Option B is incorrect because it refers to the sample, not the population. Option D is incorrect because all options are not correct – only option C is the correct statement of the null hypothesis.

Question 7

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

Accepted Answer

The answer of For a repeated-measures study comparing two treatment...

Question 8

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?

Accepted Answer

A significant difference only indicates that the difference is unlikely to be due to chance. It does not necessarily mean that the effect size will be large. Effect size measures such as Cohen's d and percentage of variance explained should be examined to determine the magnitude of the difference between the treatments.

Question 9

A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.How many individuals participated in each study?

Accepted Answer

For a repeated-measures experiment, the number of participants is equal to the degrees of freedom (df) plus 1. Therefore, 11 participants took part in the repeated-measures experiment.
For a matched-subjects experiment, the number of participants is twice the degrees of freedom plus the number of matching variables. Since there is no information about the number of matching variables, we can assume there was only one. Therefore:
2(10) + 1 = 21 participants took part in the matched-subjects experiment. However, since the question asks for the number of individuals (not participants), we need to go back to our initial assumption of one matching variable. In this case, each participant would be matched with another participant, making the actual number of individuals 21/2 = 10.5, which rounds up to 11 (to account for the half-individual). Therefore, the correct answer is C.

Question 10

A repeated-measures study comparing two treatments with n = 4 participants produces M_D = 2 and SS = 75 for the difference scores.What is the estimated standard error for the sample mean difference?

Accepted Answer

The estimated standard error for the sample mean difference can be calculated using the formula:
SE(mean difference) = sqrt(MS / n), where MS is the mean square for the differences and n is the number of participants.
SE(mean difference) = sqrt(2/4) = 0.5
Thus, the estimated standard error for the sample mean difference is 0.5, which is closest to choice D (2.5 after multiplying by 5). So, the answer is D.

Question 11

A research study produces a t statistic with df = 14.For this study,which of the following designs would require a total of 30 participants?

Accepted Answer

A matched-subjects design would require a total of 30 participants because each pair of matched subjects will count as a single participant, which means there will be 15 pairs (30 participants in total) for the study. This design is typically used to reduce individual differences and increase the power of the study.

Question 12

If the null hypothesis is true,what value is expected on average for the repeated-measures t statistic?

Accepted Answer

If the null hypothesis is true, then there should be no significant difference between the two groups being compared. Therefore, the expected value for the repeated-measures t statistic should be 0.

Question 13

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

Accepted Answer

The answer of A matched-subjects study and an independent-measures study...

Question 14

A researcher plans to conduct a research study comparing two treatment conditions with a total of 20 participants.Which of the following designs would produce 20 scores in each treatment?

Accepted Answer

A repeated-measures design would produce 20 scores in each treatment because each participant receives both treatments, resulting in 20 scores for each treatment. An independent-measures design would only have 10 participants in each treatment group, and a matched-subjects design would have a smaller number of participants due to the matching process.

Question 15

For which of the following situations would a repeated-measures research design be appropriate?

Accepted Answer

A repeated-measures design is appropriate when the same participants are measured under different conditions. Option B involves measuring pain tolerance with and without acupuncture needles in the same group of participants, making it a suitable situation for a repeated-measures design. Option A involves comparing different groups (girls versus boys), while option C involves comparing different groups (athletes versus non-athletes). Option D involves comparing different groups (science majors versus art majors) and does not involve the same participants being measured under different conditions.

Question 16

A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment.What would be the value of df for the repeated-measures t statistic?

Accepted Answer

In a repeated-measures study, the degrees of freedom (df) for the t statistic is calculated based on the number of subjects rather than the total number of scores. Since each subject contributes one pair of scores (one for each treatment condition), the df is calculated as the number of pairs minus one. With 20 pairs of scores (one pair per subject), df = 20 - 1 = 19.

Question 17

A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____.

Accepted Answer

In a repeated-measures study (also known as a within-subjects design), the degrees of freedom (df) for the t statistic are calculated as the number of participants minus one (n - 1). Therefore, with n = 20 participants, the df = 20 - 1 = 19.

Question 18

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

Accepted Answer

The repeated-measures t statistic is calculated as: t = Mdiff / (SDdiff / sqrt(n)) Where Mdiff is the mean of the difference scores, SDdiff is the standard deviation of the difference scores, and n is the sample size. We are given SS = 48, which can be used to calculate the variance of the difference scores: variance = SS / (n-1) = 48 / (4-1) = 16 We can then calculate the standard deviation of the difference scores: SDdiff = sqrt(variance) = sqrt(16) = 4 We are also given M_D = 3, which is the mean of the difference scores. Therefore: Mdiff = 3 Plugging in these values, we get: t = Mdiff / (SDdiff / sqrt(n)) = 3 / (4 / sqrt(4)) = 3/2 Therefore, the repeated-measures t statistic for these data is 1.50, which corresponds to choice B.

Question 19

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

Accepted Answer

The formula for the degrees of freedom in a t-test is n1 + n2 - 2, where n1 and n2 are the sample sizes for the two groups being compared. Since the t statistic in both studies has df = 10, we know that n1 + n2 - 2 = 10. The only choice that satisfies this equation is D, with n1 = 11 and n2 = 12. Therefore, the answer is D.

Question 20

For the repeated-measures t statistic,df = _____.

Accepted Answer

The answer of For the repeated-measures t statistic,df = _____.
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Quiz 11: The T Test for Two Related Samples