Chapter 11

The null hypothesis for a repeated-measures test states:

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

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

0

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

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

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

3

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 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

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.

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

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

n - 1

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

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

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

n=13

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

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

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

µD = 0

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

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.

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

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 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).

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

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

comparing pain tolerance with and without acupuncture needles

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

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

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

positively skewed with all values greater than or equal to zero

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

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).

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

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

The results will be influenced by order effects.

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

There are no differences between any of the population means.

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

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

the mean for a population of difference scores

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

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

19

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

2

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

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.

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

14. d. 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 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

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

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

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

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)

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

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