Question 1

If all of the participants in a repeated-measures study show roughly the same 10-point difference between treatments, then the data are likely to produce a significant value for the t statistic.

Accepted Answer

If all participants show a similar change between treatments, this suggests a consistent effect size and reduces variability in the data, increasing the likelihood of obtaining a significant t statistic.

Question 2

For a repeated-measures design, df = n₁ + n₂ - 2 for the t statistic.

Accepted Answer

The formula provided does not accurately represent the degrees of freedom (df) calculation for a t statistic in a repeated-measures design. The degrees of freedom for a repeated-measures t-test are typically calculated based on the number of subjects and the number of measurements, not using the formula provided.

Question 3

The estimated standard error in the denominator of the repeated-measures t statistic measures the average mean difference that is expected for a sample when there is a zero mean difference for the population.

Accepted Answer

The estimated standard error in the denominator of the repeated-measures t statistic indeed measures the average mean difference expected for a sample when there is a zero mean difference in the population. It quantifies the variability of the sample mean differences around the population mean difference, which is assumed to be zero under the null hypothesis.

Question 4

A repeated-measures research study comparing two treatments with a set of 10 scores in each treatment will produce a t statistic with df = 19.

Accepted Answer

In a repeated-measures design comparing two treatments, the degrees of freedom (df) for the t statistic are calculated based on the number of subjects, not the total number of scores across treatments. Since each subject contributes one pair of scores (one for each treatment), the df is based on the number of subjects minus one (N-1). If there are 10 pairs of scores (indicating 10 subjects), the df would be 10 - 1 = 9.

Question 5

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 6

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.

Question 7

If a set of n = 9 difference scores has a mean of M_D = 3.5 and a variance of s² = 36, then the standard error for the sample mean difference is 4 points.

Accepted Answer

The formula for standard error is standard deviation divided by the square root of sample size. We are given the variance (s^2) which is 36, but we need the standard deviation (s). To get s, we take the square root of the variance, which is 6. Thus, the standard error is 6 / sqrt(9) = 2. Therefore, the given statement is false.

Question 8

For a repeated-measures study, a small variance for the difference scores indicates that the treatment effect is consistent across participants.

Accepted Answer

A smaller variance for the difference scores means that the scores are clustered closely around the mean, indicating consistency in the treatment effect across all participants.

Question 9

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

Accepted Answer

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

Question 10

For a repeated-measures study, a small variance for the difference scores indicates that the treatment has little or no effect.

Accepted Answer

A small variance for the difference scores indicates that the treatment has a consistent effect, not necessarily a little or no effect. A large variance for the difference scores would indicate that the treatment has inconsistent or variable effects.

Question 11

A repeated-measures study and an independent-measures study both produce t statistics with
df = 20.The independent-measures study used more participants.

Accepted Answer

In a repeated-measures study, each participant is measured under all conditions, so the degrees of freedom (df) are based on the number of participants minus one (N-1). In an independent-measures study, the df are calculated based on the total number of participants across all groups minus the number of groups (N - k), where k is the number of groups. Therefore, for both types of studies to have the same df, the independent-measures study must have used more participants to account for the additional subtraction of the number of groups in its df calculation.

Question 12

A researcher reports df = 18 for a repeated-measures t statistic.This research study used a total of n = 19 participants.

Accepted Answer

If the researcher reported df = 18 for a repeated-measures t statistic, it means that the analysis was based on 19-1=18 degrees of freedom, which is possible for a sample size of n = 19.

Question 13

For the following data from a repeated-measures study, the sample mean difference is M_D = 4.

Accepted Answer

The answer of For the following data from a repeated-measures...

Question 14

Although the original data for a repeated-measures study consist of two scores for each participant, the calculation of the mean and variance are done with only one score for each participant.

Accepted Answer

The mean and variance for a repeated-measures study are calculated with the scores for each participant across all time points or conditions, thus resulting in a single mean and variance for each participant.

Question 15

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

Accepted Answer

The estimated standard error in the denominator is computed entirely from the sample data in the repeated-measures t statistic.

Question 16

In general, as the variance of the difference scores increases, the likelihood of finding a significant difference also increases.

Accepted Answer

As the variance of the difference scores increases, it generally becomes harder to find a significant difference because increased variance leads to a larger standard error, which can make it more difficult to detect a true effect in statistical tests.

Question 17

The repeated-measures t statistic is used with a matched-subjects design even though the design uses two separate samples.

Accepted Answer

In a matched-subjects design, participants in one sample are matched with participants in another sample based on certain characteristics, creating pairs. The repeated-measures t statistic is appropriate because it accounts for the pairing, treating the data as dependent samples.

Question 18

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.The repeated-measures t statistic for this study has df = 29.

Accepted Answer

The degrees of freedom (df) for a repeated-measures t-test is calculated based on the number of subjects, not the total number of scores. For n = 15 participants, df = n - 1, so df = 14, not 29.

Question 19

If a set of n = 9 difference scores has a mean of M_D = 3.5 and a variance of s² = 36, then the sample will produce a repeated-measures t statistic of t = 3.5/2.

Accepted Answer

The answer of If a set of n = 9...

Question 20

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

In a repeated-measures design, each participant is measured in both conditions. Therefore, the study would only require 30 participants, not 60.

Quiz 11: The T Test for Two Related Samples