Question 1

In a repeated-measures study comparing two treatments with a sample of n = 15 participants,the researcher measures two scores for each individual to obtain a total of 30 scores and the repeated-measures t statistic has df = 29.

Accepted Answer

In a repeated-measures study, the degrees of freedom (df) for the t statistic are calculated based on the number of participants, not the total number of scores. Since each participant is measured twice, the df would be n - 1, which is 15 - 1 = 14, not 29.

Question 2

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

Accepted Answer

A confidence interval using the repeated-measures t statistic estimates the mean for a population of difference scores, reflecting the average change in measurements taken from the same subjects under two different conditions or at two different times.

Question 3

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

Accepted Answer

Repeated-measures studies involve measuring the same group of participants multiple times. This can lead to order effects, where the results are influenced by the order of the treatments or measures. This is a serious concern because it can make it difficult to determine the true effect of the treatment independent of order effects. Factors such as practice, fatigue or learning can also have an impact. Therefore, B is the best choice as all of the other options are not necessarily true for all repeated-measures studies.

Question 4

A researcher would like to compare two treatment conditions with a set of 30 scores in each treatment.If a repeated-measures design is used,the study will require n = 60 participants.

Accepted Answer

A repeated-measures design is a within-subjects design, meaning that each participant is exposed to both conditions. Therefore, the study would only require 30 participants if each participant undergoes both treatments.

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 MD = 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?

Accepted Answer

The formula for calculating the confidence interval for a population mean difference is:

CI = (MD - tα/2 *SEMD, MD + tα/2 *SEMD)

where 
MD = sample mean difference (0.60 in this case)
tα/2 = t-value for the level of confidence (80% confidence interval, so t-value from t-distribution table with df = n-1 = 8 and α/2 = 0.10)
SEMD = standard error of the mean difference

SEMD = s/√n = 0.09/√9 = 0.03

Plugging in the values, we get:

CI = (0.60 - 1.397*0.03, 0.60 + 1.397*0.03)
   = (0.55, 0.65)

Therefore, the 80% confidence interval for the population mean difference in GPA before and after the workshop is (0.55, 0.65).

Choice C is the closest option to this calculated interval.

Question 6

Which of the following will not increase the width of a confidence interval?

Accepted Answer

Increasing the sample mean will not increase the width of a confidence interval. This is because a larger sample mean indicates a greater level of accuracy, which leads to a narrower confidence interval. The other options will all increase the width of a confidence interval.

Question 7

In a repeated measures study,the null hypothesis says that the mean for the sample of difference scores is equal to zero.

Accepted Answer

The answer of In a repeated measures study,the null hypothesis...

Question 8

Although a repeated-measures study measures two scores for each participant,the sample mean and variance are computed using only one score for each participant.

Accepted Answer

In a repeated-measures study, each participant is measured multiple times, resulting in multiple scores. The sample mean and variance are calculated using all of the scores for each participant, not just one.

Question 9

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?

Accepted Answer

The wider the variance (s2), the wider the confidence interval. Therefore, option D with MD = 3 and s2 = 20 will produce the widest 90% confidence interval.

Question 10

For the repeated-measures t statistic,the value of the estimated standard error in the denominator is computed entirely from the sample data.

Accepted Answer

The estimated standard error in the denominator of the repeated-measures t statistic is computed entirely from the sample data using a formula that takes into account the sample size, the standard deviation of the differences between the paired observations, and the correlation between the paired observations.

Question 11

Which of the following describes the effect of an increase in the variance of the difference scores in a repeated-measures design?

Accepted Answer

The answer of Which of the following describes the effect...

Question 12

Which of the following describes the effect of increasing sample size in a repeated-measures design?

Accepted Answer

Increasing sample size in a repeated-measures design typically does not increase measures of effect size, as effect size is based on the magnitude of the difference between groups or conditions and is not affected by sample size. However, increasing sample size can increase the likelihood of rejecting the null hypothesis in statistical tests, as larger samples increase power and reduce the chance of type II errors. Therefore, the correct choice is C, which states that there is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.

Question 13

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.What is this problem is called?

Accepted Answer

The problem described is known as order effects, where the order in which the treatments are completed influences the participant's scores. This is a common issue in repeated-measures experiments and needs to be controlled for to ensure accurate results. Options A, C, and D are not relevant to this issue.

Question 14

One concern for a repeated-measures study is that the participants in one treatment may have different characteristics than the participants in the other treatment.

Accepted Answer

In a repeated-measures study, the same participants are used in all treatment conditions, which eliminates concerns about differences in characteristics between groups.

Question 15

A repeated-measures study and matched-subjects study both produce t statistics with df = 20.The repeated-measures study used more participants than the matched-subjects study.

Accepted Answer

The degrees of freedom for a t-test depend on the sample size, with larger sample sizes leading to higher degrees of freedom. Therefore, if both the repeated-measures study and matched-subjects study had the same number of participants, they would have the same degrees of freedom. The fact that the repeated-measures study used more participants does not necessarily mean that they will have higher degrees of freedom, as they could have used a repeated-measures design with fewer independent groups or conditions.

Question 16

The estimated standard error in the denominator of the repeated-measures t statistic measures the typical mean difference that is expected for a sample selected from a population with a zero mean difference.

Accepted Answer

The estimated standard error in the denominator of the repeated-measures t statistic measures the variability of the mean difference scores in the sample, assuming a zero mean difference in the population. Therefore, it is true that the typical mean difference expected for a sample selected from a population with a zero mean difference is being measured.

Question 17

Compared to an independent-measures design,a repeated-measures study is more likely to find a significant effect because it reduces the contribution of variance due to ______.

Accepted Answer

A repeated-measures study reduces the contribution of variance due to individual differences because the same participants are used in all conditions, thereby controlling for variability among participants.

Question 18

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

Accepted Answer

A repeated-measures design is most advantageous when there are few subjects available and individual differences among them are large. This design allows each participant to serve as their own control, which effectively reduces the variability due to individual differences, making it easier to detect any treatment effects with a smaller sample size.

Question 19

For the following data from a repeated-measures study,the sample mean difference is MD = 1.
 $$\begin{array} { c r r } 
\text { Participant } & X _ { 1 } & X _ { 2 } \
\hline \mathrm { A } & 1 & 5 \
\mathrm {~B} & 4 & 6 \
\mathrm { C } & 5 & 2
\end{array}$$

Accepted Answer

To find the sample mean difference, we need to calculate the difference between X1 and X2 for each participant, then calculate the mean of those differences. For participant A, the difference is 5 - 1 = 4. For participant B, the difference is 6 - 4 = 2. For participant C, the difference is 2 - 5 = -3. The mean of these differences is (4 + 2 - 3) / 3 = 1. Therefore, the sample mean difference is MD = 1.

Question 20

A repeated-measures study and an independent-measures study both produce a t statistic with df = 20.The repeated-measures study used more subjects than the independent-measures study.

Accepted Answer

In a repeated-measures study, each subject is measured more than once, which means the number of subjects can be less to achieve the same degrees of freedom (df) as an independent-measures study, where each measurement comes from a different subject.

Quiz 11: The t Test for Two Related Samples