### Repeated-Measures T Statistic, Rejecting The Null Hypothesis, Repeated-Measures Study

The key terms in these Statistic chapters include Repeated-Measures Study, Repeated Measures T Statistic, Variance, Rejecting The Null, Mean, Standard Error, Rejecting The Null Hypothesis, Sample, Population, Research Study.

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

**True**

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

**True**

For measures study, if other factors are held constant, then an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

**True**

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 small variance for the difference scores and a small standard error**

The following data were obtained from a repeated-measures research study. What is the value of MD for these data?

Subject 1st 2nd

#1 10 15

#2 4 8

#3 7 5

#4 6 11

**3**

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

**True**

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

**True**

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 small variance for the difference scores and a small standard error**

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

**d = 5/10**

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

**False**

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.

**True**

A repeated-measures study with a sample of n = 16 participants produces a repeated-measures t = 2.00. If effect size is measured using r2, then r2 = 4/20.

**False**

For a repeated-measures study, as the sample mean difference increases, the likelihood of rejecting the null hypothesis also increases.

**True**

For a repeated-measures design, the sample mean difference is always located exactly in the center of the confidence interval estimate for the population mean difference.

**True**

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

**It will decrease (move toward 0 at the center of the distribution).**

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.

**True**

The following X and Y scores from a research study produced SS X = 2 and SP = 8. What is the regression equation for predicting Y?

X Y

1 2

2 3

3 10

**Y = 4X – 3**

Which of the following describes the effect of an increase in the variance of the difference scores?

**Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.**

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.

**False**

Repeated-measures designs are particularly well-suited to research studies examining learning or other changes that occur over time.

**True**

Which of the following best describes the Pearson correlation for these data?

X Y

2 5

5 1

3 4

4 2

**Negative**

One concern for a repeated-measures study is that a participant’s score in one treatment may be influenced by practice or experience gained in a previous treatment.

**True**

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?

**Order effects**

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

**The results will be influenced by order effects.**

For a repeated-measures study, if other factors are held constant, then an increase in the size of the sample will increase the likelihood of finding a significant treatment effect.

**True**

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

**True**

For a repeated-measures study, if other factors are held constant, then an increase in the size of the sample will increase measures of effect size.

**False**

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

**4/2**

A repeated-measures research study uses a total of 20 participants to compare two treatment conditions. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.729.

**True**

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

**False**

An analysis of regression is used to test the significance of a linear regression equation based on a sample of n = 20 individuals. What are the df values for the F-ratio?

**1,18**

Suppose the correlation between height and weight for adults is r = +0.40. Which proportion (or percent) of the variability in weight can be explained by its relationship with height?

**16%**

For which of the following Pearson correlations would the data points be clustered most closely around a straight line?

**r = – 0.70**

Under which circumstances is the phi-coefficient used?

**When both variables are dichotomous**

For a two-tailed hypothesis test evaluating a Pearson correlation, what is stated by the null hypothesis?

**The population correlation is zero.**

The following X and Y scores from a research study produced SS X = 2 and SP = 8. What is the regression equation for predicting Y?

X Y

1 2

2 3

3 10

**Y = 4X – 3**

Which of the following best describes the Pearson correlation for these data?

X Y

2 5

5 1

3 4

4 2

What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?

**The Spearman correlation**

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 small variance for the difference scores and a small standard error**

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

**True**

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

**True**

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

**False**

For a repeated-measures study, as the sample mean difference increases, the likelihood of rejecting the null hypothesis also increases.

**True**

For a repeated-measures design, the sample mean difference is always located exactly in the center of the confidence interval estimate for the population mean difference.

**True**

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

**It will decrease (move toward 0 at the center of the distribution).**

Which of the following describes the effect of an increase in the variance of the difference scores?

**Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.**

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.

**False**

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

**4/2**

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

**False**

Suppose the correlation between height and weight for adults is r = +0.40. Which proportion (or percent) of the variability in weight can be explained by its relationship with height?

**16%**

For which of the following Pearson correlations would the data points be clustered most closely around a straight line?

**r = – 0.70**

The following X and Y scores from a research study produced SS X = 2 and SP = 8. What is the regression equation for predicting Y?

X Y

1 2

2 3

3 10

**Y = 4X – 3**

Which of the following best describes the Pearson correlation for these data?

X Y

2 5

5 1

3 4

4 2

**Negative**