### Repeated Measures T Test & Research Design, Grade Point Average, The Null Hypothesis

The key terms in these Statistic Chapters include Variance, Repeated Measures T Test, Research Design, Grade Point Average, Rejecting the Null Hypothesis – Researcher Statistic

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

19

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

Comparing pain tolerance with and without acupuncture needles

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

11 for repeated, and 22 for matched

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

A repeated-measures design

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

#### 3

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?

df=18

A repeated-measures study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study?

17 for repeated-measures and 18 for independent-measures

A matched-subjects study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study?

34 for matched-subjects and 18 for independent-measures

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

n – 1

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

µD = 0

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

0

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

#### 19

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

Comparing pain tolerance with and without acupuncture needles

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

11 for repeated, and 22 for matched

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

A repeated-measures design

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

3

The null hypothesis for a repeated-measures test states:

The entire population will have a mean difference of μD = 0.

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

#### 2

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 = 288. What is the estimated standard error for the sample mean difference?

d. 2

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 = 4 with SS = 12 for the difference scores. What is the estimated standard error for the sample mean difference?

1

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

If a repeated-measures study shows a significant difference between two treatments with α = .01, then you can be sure that _____.

A significant effect does not necessarily mean that the effect size will be large.

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

For a repeated-measures study comparing two treatment conditions, a researcher obtains Cohen’s d = 0.50 for a sample of n = 4 scores with a variance of s2 = 16. What is the value of the sample mean?

A researcher obtains t(20) = 2.00 and MD = 9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?

#### 4/24

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.

Reject the null hypothesis with a one-tailed test but fail to reject with two tails.

A researcher obtains t = 2.35 for a repeated-measures study using a sample of
n = 8 participants. Based on this t value, what is the correct decision for a two-tailed test?

Fail to reject the null hypothesis with either α = .05 or α = .01

A research report describing the results from a repeated-measures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, you can conclude that a total of ____ individuals participated in the research study

#### 11

A research report describing the results from a repeated-measures t test states, “t(22) = 1.71, p > .05.” From this report you can conclude that the outcome of the hypothesis test was ______.

To fail to reject the null hypothesis with a sample of n = 23 participants

A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study?

n=13

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

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

A researcher uses a repeated-measures design to compare individuals’ performance before treatment with their performance after treatment. If all of the participants show improved performance of 8 or 9 points after treatment, then the researcher should find ______.

The variance of the difference scores is near zero

In general, what is the effect of an increase in the variance for the sample of difference scores?

An increase in the standard error and a decrease in the value of t

In general, what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?

A large number of scores and a small variance

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

What is indicated by a large variance for a sample of difference scores?

An inconsistent treatment effect and a low likelihood of a significant difference

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 other factors are held constant, which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?

n = 30 and SS = 10 for the difference scores

Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis?

Increase the sample mean difference

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

The results will be influenced by order effects.

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

#### Individual differences

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

When very few subjects are available and individual differences are large

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. This problem is called ______.

##### Order effects

Repeated Measures T Test

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

The mean for a population of difference scores

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?

µD = 0.60 + 0.10(1.397)

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

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

#### True

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?

##### MD = 5 with s2 = 5 for the difference scores

Briefly explain the advantages and disadvantages of using a repeated-measures design as opposed to an independent-measures design.

A repeated measures design tends to be more precise or more powerful than an independent measures design because it eliminates variability due to individual differences. Also, a repeated-measure design uses fewer subjects than an independent-measures design. However, the results from a repeated-measures experiment can be confounded by time-related factors and order effects

Describe the circumstances under which you should use ANOVA instead of t tests, and explain why t tests are inappropriate in these circumstances.

ANOVA should be used when there are more than two treatment conditions. In this situation it would require several t tests to compare all the treatments, and the more tests that are done the more risk there is for a Type I error

Describe the circumstances in which post tests are used and explain why these tests are necessary.

Post tests are done after an analysis of variance that rejects the null hypothesis and is comparing three or more treatments. The decision to reject H0 simply indicates that at least one of the treatment means is different from another. The purpose of the post tests is to determine exactly which treatment means are different.

What value is expected, on average, for the F ratio in ANOVA when the null hypothesis is true? Explain why this value is expected.

When the null hypothesis is true, the F ratio is expected to be near 1.00. The structure of the F ratio is balanced so that the numerator and denominator are measuring identical sources of variance if the treatment effect is zero (H0 is true).

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?

#### Using several t tests increases the risk of a Type I error.

What is stated by the null hypothesis (H0) for an ANOVA?

There are no differences between any of the population means.

What is stated by the alternative hypothesis (H1) for an ANOVA?

At least one of the population means is different from another mean

Which of the following describes a typical distribution of F ratios?

Positively skewed with all values greater than or equal to zero

Describe the circumstances under which you should use ANOVA instead of t tests, and explain why t tests are inappropriate in these circumstances.

inappropriate in these circumstances

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