Question 1

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, there should be no significant difference between the two sets of data, leading to an average t value of 0.

Question 2

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

Accepted Answer

The df for the repeated-measures t statistic is equal to the number of participants minus 1, which is then multiplied by the number of conditions minus 1 (df = (n-1)*(k-1)). In this case, since there are 20 scores in each treatment and two treatments, there are 40 total scores. This means there are 40/2 = 20 participants. Therefore, the df for the repeated-measures t statistic is (20-1)*(2-1) = 19.

Question 3

The following data were obtained from a repeated-measures research study.What is the value of MD for these data? $$\begin{array} { c r r } 
\text { Subject } & \text { 1st } & 2 \text { nd } \
\hline \# 1 & 10 & 15 \
\# 2 & 4 & 8 \
\# 3 & 7 & 5 \
\# 4 & 6 & 11
\end{array}$$

Accepted Answer

MD (mean difference) is calculated by finding the difference between the two measurements for each subject, summing these differences, and then dividing by the number of subjects. The differences are 5, 4, -2, and 5. The sum is 12, and dividing by 4 subjects gives an MD of 3.

Question 4

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 or at different time points. In the case of comparing pain tolerance with and without acupuncture needles, it would be appropriate to use a repeated-measures design because the same participants would be measured with and without the needles. For the other situations, different groups of participants are being compared rather than the same participants being measured multiple times, so a repeated-measures design would not be appropriate.

Question 5

The null hypothesis for a repeated-measures test states:

Accepted Answer

The null hypothesis for a repeated-measures test is that the entire population will have a mean difference of μD = 0. This means that the difference between the pairs of measurements for each individual in the population is expected to be zero, on average. Therefore, option C is the correct choice. Options A and B are incorrect because they refer to individual or sample differences, respectively, instead of population differences. Option D is incorrect because only option C is correct.

Question 6

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 7

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

The answer of A research study produces a t statistic...

Question 8

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

In a repeated-measures study with 10 participants comparing two conditions, each participant provides one score per condition, resulting in 20 scores measured. However, only the difference scores (10) are used to compute the sample mean and variance.

Question 9

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

Accepted Answer

The answer of For a repeated-measures study,if the null hypothesis...

Question 10

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces a mean of M₁ = 18 with SS = 24 for the scores in the first treatment,a mean of M₂ = 14 with SS = 18 for the scores in the second treatment,and a mean of MD = 4 with SS = 12 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 (MD) is calculated using the formula SE = sqrt(SS/n), where SS is the sum of squares for the difference scores, and n is the sample size. Substituting the given values, SE = sqrt(12/4) = sqrt(3) ≈ 1.74, which rounds to 1.

Question 11

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 is that there is no difference between the means of two related groups, which can be expressed as the mean difference (µD) being equal to zero. Therefore, choice B (µD = 0) is the correct option. Choice A (MD = 0) is incorrect because it does not specify that the means are related, while choices C (µ1 = µ2) and D (M1 = M2) are incorrect because they do not account for the fact that the means are from the same group at different time points or conditions.

Question 12

A repeated-measures study comparing two treatments with n = 4 participants produces MD = 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 is calculated using the formula SE = sqrt(SS/n), where SS is the sum of squares for the difference scores, and n is the number of participants. Plugging in the given values, SE = sqrt(75/4) = sqrt(18.75) ≈ 4.33. However, none of the provided options exactly match this calculation. The closest option, based on the provided values and typical calculation methods, would be D) 2.5, assuming there might have been a misunderstanding in the calculation process or a typo in the options.

Question 13

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 in this design, each participant is measured under both treatment conditions, resulting in a set of scores for each participant in each treatment. Therefore, with 20 participants, there would be 20 scores in each treatment condition. The other options (independent-measures and matched-subjects designs) would not necessarily result in 20 scores in each treatment condition, as both of these designs involve comparing two separate groups of participants rather than having each participant provide scores in both treatment conditions.

Question 14

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

For a repeated-measures study, df = n - 1, so n = 11. For an independent-measures study, df = n1 + n2 - 2, so n1 + n2 = 12, assuming equal group sizes, n1 = n2 = 6, totaling 12 individuals.

Question 15

What is the value of the estimated standard error for the following set of D-scores? Scores: 2,2,10,2

Accepted Answer

The answer of What is the value of the estimated...

Question 16

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

The degrees of freedom for both the repeated-measures and matched-subjects t-tests is calculated using n-1, where n is the number of individuals. Since both tests have the same df value of 10, we can set up the equation as follows: 
n-1 = 10 
Solving for n: 
n = 11

Therefore, the number of individuals in the repeated-measures experiment is 11. For the matched-subjects experiment, we need to remember that the t-test is comparing differences between pairs of individuals. This means that each individual in the study is paired with another individual who is similar in some way (e.g. age, gender, etc.). Since we have pairs of individuals, the total number of individuals in the study is twice the number of pairs. If we assume that each pair consists of one individual in the treatment group and one individual in the control group, then we can set up the equation as follows: 
2n-2 = 10 
Solving for n: 
n = 6

Since we have 6 pairs of individuals, the total number of individuals in the matched-subjects experiment is 2n, or 12. Thus, the best choice is C, with 11 individuals in the repeated-measures experiment and 12 individuals in the matched-subjects experiment.

Question 17

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

Accepted Answer

The degrees of freedom (df) for a repeated-measures t-test is calculated as the number of participants minus one (n - 1). For n = 20, df = 20 - 1 = 19.

Question 18

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

Accepted Answer

The degrees of freedom (df) for a repeated-measures t-test is calculated as n - 1, where n is the number of pairs of scores.

Question 19

For a repeated-measures study comparing two treatments with a sample of n = 9 participants,the difference scores have a mean of MD = 4.90 with SS = 72.What is the estimated standard error for the sample mean difference?

Accepted Answer

The estimated standard error for the sample mean difference is calculated using the formula: SE = sqrt(SS / (n(n-1))). Plugging in the values: SE = sqrt(72 / (9(9-1))) = sqrt(72 / 72) = sqrt(1) = 1.

Question 20

The following data were obtained from a repeated-measures research study.What is the value of SS for the difference scores? $$\begin{array} { l c c } 
\text { Subject } & 1 \text { st } & 2 \text { nd } \
\hline \# 1 & 10 & 11 \
\# 2 & 4 & 6 \
\# 3 & 7 & 9 \
\# 4 & 6 & 5
\end{array}$$

Accepted Answer

The difference scores are 1, 2, 2, -1. The mean of these scores is 1. The SS is calculated as the sum of squared deviations from the mean: (1-1)² + (2-1)² + (2-1)² + (-1-1)² = 0 + 1 + 1 + 4 = 6.

Quiz 11: The t Test for Two Related Samples