Exam chapter 11 2016, questions and answers PDF

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Chapter 11 - estimation. T/F questions and Short Answer with Solutions...

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Chapter 11: The t Test for Two Related Samples Chapter Outline 11.1 Introduction to Repeated-Measures Designs The Matched-Subjects Design 11.2 The t Statistic for a Repeated-Measures Research Design Difference Scores: The Data for a Repeated-Measures Study The Hypotheses for a Related-Samples Test The t Statistic for Related Samples 11.3 Hypothesis Tests and Effect Size for the Repeated-Measures Design Measuring Effect Size for the Repeated-Measures t In the Literature - Reporting the Results of a Repeated-Measures t Test Descriptive Statistics and the Hypothesis Test Variability as a Measure of Consistency for the Treatment Effect Directional Hypotheses and One-Tailed Tests 11.4 Uses and Assumptions for Repeated-Measures t Tests Repeated-Measures versus Independent-Measures Designs Time-Related Factors and Order Effects Assumptions of the Related-Samples t Test

Learning Objectives and Chapter Summary 1. Students should understand the structure of a research study that produces data appropriate for a repeated-measures t hypothesis test. A repeated-measures (or within-subjects) research study uses a single sample that is measured in all of the different treatment conditions that are being compared. For the repeated-measures t test the sample is measured in two treatment conditions (exactly two scores for each individual), and the scores in each condition must be numerical values that allow calculation of the sample mean and the sample variance. The repeatedmeasures t statistic is also used for matched-subjects designs where the individuals in one treatment are matched, one to one, with the individuals in the second treatment.

Instructor Notes - Chapter 11 - page 152

2. Students should be able to use the repeated-measures t statistic to test hypotheses about the mean difference between two treatment conditions. The repeated-measures t test begins by computing a difference score (D) that measures the difference between the two scores obtained for each individual. The sample mean for the difference scores is used to test a hypothesis about the corresponding population mean difference. The null hypothesis states that the population mean difference is zero (there is no difference between the two treatment conditions). Because the repeated-measures test uses only one sample (of difference scores) to test a hypothesis about one population (of difference scores), the t statistic has exactly the same structure as the single-sample t in Chapter 9. 3. Students should be able to evaluate the size of the mean difference by computing either Cohen’s d or r2 (the percentage of variance accounted for), and they should be able to describe the size of the mean difference by constructing a confidence interval. Cohen’s d measures the standardized distance between two distributions: The null distribution that is centered at zero and the treatment distribution that is centered at M D. The value of r2 is a measure of how much of the variability in the scores can be attributed to the treatment effect. For example, Figure 11.4 shows a sample of difference scores centered at MD = 3.00. If there were no treatment effect, the scores should be centered around zero. In this case, the treatment has shifted the scores to the right away from zero which increases the deviations from μD = 0. It is this increase in deviations (actually the increase in SS) that is being measured by r2. If you compute the deviations from zero and calculate the sum of squared deviations, you will obtain SS = 99. Then, remove the treatment effect by subtracting 3 points from each score so that the scores are centered around zero. Again, find the deviations from zero and compute the sum of squared deviations. This time you obtain SS = 18. Removing the treatment effect reduces the SS value by 81 points (from 99 to 18). Expressed as a percentage, this is 81/99 = 0.818 or 81.8% which is exactly the same value obtained with the r2 formula. A confidence interval is not a true measure of effect size but it is a convenient way to describe the size of the mean difference. 4. Students should understand the relative advantages and disadvantages of repeated-measures studies compared to independent-measures studies, and should recognize the situations where each type of study is appropriate. Because a repeated-measures study uses the same group of individuals in all of the different treatments, it typically requires fewer participants than are needed for an independent-measures study, which requires a separate sample for each treatment. The main advantage of a within-subjects design is that it eliminates or reduces the problems caused by individual differences. For example, a repeated-measures design guarantees equivalent groups for all of the different treatments because the same group is Instructor Notes - Chapter 11 - page 153

used in all of the treatments. An independent-measures study on the other hand compares different groups, so there is always the risk that one group may be smarter, or older, or faster than the other group. The main disadvantage of a within-subjects design is the risk that carry-over effects or progressive error may distort the research results. (Participating in one treatment may influence the scores in a later treatment.) These effects cannot occur in an independentmeasures study because each individual participates in only one treatment condition.

Other Lecture Suggestions 1. It should be obvious but it is worth pointing out to students that the repeated-measures t statistic is simply the single-sample t (Chapter 9) applied to a new research situation. Specifically, the repeated-measures t uses a sample of difference scores to test a hypothesis about the population of difference scores. Note that one sample is being used to evaluate a hypothesis about one unknown population. 2. In the context of a repeated-measures research study, the sample variance becomes a relatively concrete and easy to understand concept. In particular, the sample variance simply describes the consistency of the treatment effect. For example, if a treatment consistently adds around 10 points to each individual’s score, then the set of difference scores will be clustered around a mean of MD = 10 with a very small variance. In this situation, the treatment effect is easy to see (everyone’s score increases by about 10 points) and the treatment effect is likely to be significant. On the other hand, if a treatment has no consistent effect, the difference scores will be widely scattered with a large variance. For some individuals the treatment produces an increase of 10 or 15 points, for others the treatment has little or no effect (scores around zero), and for others the treatment seems to decrease scores (negative D scores). Where there is no consistent effect (large variance) it is difficult to see any treatment effect in the data and it is more likely that a hypothesis test will find no significant effect. This concept is demonstrated on pages 319-320 using the samples in figures 11.4 and 11.5. 3. The same values of n and SS that produced whole-number answers in Chapter 9 can be used to produce easy classroom examples for Chapter 11. n = 9 and SS = 72 produce a variance of 9 and a standard error of 1 n = 16 and SS = 60 produce a variance of 4 and a standard error of 0.5 n = 16 and SS = 960 produce a variance of 64 and a standard error of 2 n = 16 and SS = 6000 produce a variance of 400 and a standard error of 5 n = 25 and SS = 2400 produce a variance of 100 and a standard error of 2

Instructor Notes - Chapter 11 - page 154

Exam Items for Chapter 11

Multiple-Choice Questions 1. For which of the following situations would a repeated-measures research design be appropriate? a. comparing mathematical skills for girls versus boys at age 10 b. comparing pain tolerance with and without acupuncture needles c. comparing self-esteem for students who participate in school athletics versus those who do not d. comparing verbal solving skills for science majors versus art majors at a college 2. 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. an independent-measures design b. a repeated-measures design c. a matched-subjects design d. all of the other options require only 20 participants 3. The following data were obtained from a repeated-measures research study. What is the value of MD for these data? a. 3 Subject 1st 2nd b. 3.5 #1 10 15 c. 4 #2 4 8 d. 4.5 #3 7 5 #4 6 11 4. A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____. a. 9 b. 19 c. 20 d. 39 5. A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10. How many individuals participated in each study? a. 11 for repeated, and 11 for matched b. 11 for repeated, and 12 for matched c. 11 for repeated, and 22 for matched d. 12 for repeated, and 12 for matched Instructor Notes - Chapter 11 - page 155

6. (www) 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 repeatedmeasures t statistic? a. df = 18 b. df = 19 c. df = 38 d. df = 39 7. A repeated-measures study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study? a. 18 for repeated-measures and 17 for independent-measures b. 18 for repeated-measures and 18 for independent-measures c. 17 for repeated-measures and 17 for independent-measures d. 17 for repeated-measures and 18 for independent-measures 8. A matched-subjects study and an independent-measures study both produced a t statistic with df = 16. How many individuals participated in each study? a. 17 for matched-subjects and 17 for independent-measures b. 17 for matched-subjects and 18 for independent-measures c. 18 for matched-subjects and 18 for independent-measures d. 34 for matched-subjects and 18 for independent-measures 9. For the repeated-measures t statistic, df = _____. a. n1 + n2 – 2 b. (n1 – 1) + (n2 – 1) c. n – 1 d. n1 + n2 – 1 10. (www) Which of the following is the correct null hypothesis for a repeated-measures t test? a. MD = 0 b. µD = 0 c. µ1 = µ2 d. M1 = M2 11. If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic? a. 0 b. 1 c. 1.96 d. t > 1.96

Instructor Notes - Chapter 11 - page 156

12. The null hypothesis for a repeated-measures test states: a. Each individual will have a difference score of D = 0. b. The overall sample will have a mean difference of MD = 0. c. The entire population will have a mean difference of μD = 0. d. All of the other options are correct. 13. What is the value of the estimated standard error for the following set of D-scores? a. 3 Scores: 2, 2, 10, 2 b. 3 c. 4 d. 2 14. (www) 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? a. 36 b. 36/8 = 4.5 c. 4 d. 2 15. 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? a. 4 b. 3 c. 2 d. 1 16. (www) 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? a. 4/2 b. 4/4 c. 4/6 d. 4/36 17. If a repeated-measures study shows a significant difference between two treatments with α = .01, then you can be sure that _____. a. the value of Cohen’s d is large. b. the percentage of variance explained (r2) is large c. both Cohen’s d and r2 are large d. A significant effect does not necessarily mean that the effect size will be large.

Instructor Notes - Chapter 11 - page 157

18. 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? a. d = 5/10 b. d = 5/100 c d = 25/100 d. cannot determine without knowing the sample size 19. 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. MD = 2 b. MD = 4 c. MD = 8 d. MD = 16 20. (www) 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? a. 9/20 b. 9/29 c. 4/13 d. 4/24 **21. 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. a. Reject the null hypothesis with a one-tailed test but fail to reject with two tails. b. Reject the null hypothesis with either a one-tailed or a two-tailed test. c. Fail to reject the null hypothesis with either a one-tailed or a two-tailed test. d. Fail to reject the null hypothesis with a one-tailed test but reject with two tails. **22. (www) 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? a. reject the null hypothesis with α = .05 but not with α = .01 b. reject the null hypothesis with either α = .05 or α = .01 c. fail to reject the null hypothesis with either α = .05 or α = .01 d. cannot make a decision without additional information

Instructor Notes - Chapter 11 - page 158

23. (www) 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 . a. 9 b. 10 c. 11 d. 12 24. 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 ______. a. to reject the null hypothesis with a sample of n = 23 participants b. to fail to reject the null hypothesis with a sample of n = 23 participants c. to reject the null hypothesis with a sample of n = 22 participants d. to fail to reject the null hypothesis with a sample of n = 22 participants 25. A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study? a. n = 11 b. n = 13 c. n = 24 d. n = 25 26. (www) In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic? a. It will increase (move farther toward the tail of the distribution). b. It will decrease (move toward 0 at the center of the distribution). c. It will stay the same - the t statistic is not affected by the variance of the difference scores. d. It may increase or may decrease. There is no consistent relationship between variance and the size of the t statistic. 27. 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 ______. a. a sample mean difference near zero b. a t statistic near zero c. the variance of the difference scores is near zero d. None of the other options is correct.

Instructor Notes - Chapter 11 - page 159

28. In general, what is the effect of an increase in the variance for the sample of difference scores? a. an increase in the standard error and an increase in the value of t b. an increase in the standard error and a decrease in the value of t c. a decrease in the standard error and an increase in the value of t d. a decrease in the standard error and a decrease in the value of t 29. In general, what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test? a. a large number of scores and a large variance b. a large number of scores and a small variance c. a small number of scores and a large variance d. a small number of scores and a small variance 30. (www) What is indicated by a large variance for a sample of difference scores? a. a consistent treatment effect and a high likelihood of a significant difference b. a consistent treatment effect and a low likelihood of a significant difference c. an inconsistent treatment effect and a high likelihood of a significant difference d. an inconsistent treatment effect and a low likelihood of a significant difference 31. 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. a small variance for the difference scores and a small standard error b. a small variance for the difference scores and a large standard error c. a large variance for the difference scores and a small standard error d. a large variance for the difference scores and a large standard error 32. 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? a. n = 15 and SS = 10 for the difference scores b. n = 15 and SS = 100 for the difference scores c. n = 30 and SS = 10 for the difference scores d. n = 30 and SS = 100 for the difference scores 33. Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis? a. decrease the sample size b. increase the sample mean difference c. increase the sample variance d. None of the other 3 options would increase the likelihood.

Instructor Notes - Chapter 11 - page 160

34. Which of the following possibilities is a serious concern with a repeated-measures study? a. You will obtain negative values for the difference scores. b. The results will be influenced by order effects. c. The mean difference is due to individual differences rather than treatment differences. d. All of the other options are major concerns. 35. (www) 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 ______. a. MD b. degrees of freedom c. the effect of the treatment d. individual differences 36. For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design? a. when many subjects are available and individual differences are small b. when very few subjects are available and individual differences are small c. when many subjects are available and individual differences are large d. when very few subjects are available and individual differences are large 37. 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 ______. a. individual differences b. order effects c. homogeneity of variance d. bi-treatment effect 38. What value is estimated with a confidence interval using the repeated-measures t statistic? a. the mean for a sample of difference scores b. the mean for a population of difference scores c. the difference between two population means d. the difference between two sam...