Questions and Answers of Fundamentals Of Statistics

One hundred years ago Bleuler (1911) described schizophrenia as being characterized by a lack of connections between associations in memory. Suddath, Christison, Torrey, Casanova, and Weinberger
Write up a brief summary of the study in Exercise 20.10.I frequently ask you to use SPSS or R to solve a problem. You should have no problem with SPSS if you stick with the “Legacy” analyses. You
The history of statistical hypothesis testing really began with a tea-tasting experiment (Fisher, 1935), so it seems fitting for this book to end with one. (This is also a fitting ending because
Use R, SPSS, or another program to reproduce the results shown in Figure 9.5. You can modify the R code given in Section 9.4.Section 9.4 You might expect that we could use the covariance as a measure
In Section 6.4 I said that T scores are designed to have a mean of 50 and a standard deviation of 10 and that the Achenbach Youth Self-Report measure produces T scores. The data in Figure 6.3 do not
Diagram the situation described in Exercise 15.3 along the lines of Figure 15.2.Exercise 15.3In Section 12.3 we looked at a set of data on whether children who are stressed from their
In Exercise 15.3 what sample sizes would be needed to raise power to 0.70, 0.80, and 0.90?Exercise 15.3In Section 12.3 we looked at a set of data on whether children who are stressed from their
Following on from Exercise 15.3, suppose that my colleagues were tired of having children tell them what they think we want to hear and gave them a heart-to-heart talk on the necessity of accurate
Diagram the situation described in Exercise 15.6 along the lines of Figure 15.2.Exercise 15.6Following on from Exercise 15.3, suppose that my colleagues were tired of having children tell them what
How many subjects would we need in Exercise 15.6 to have power 5 .80?Exercise 15.6Following on from Exercise 15.3, suppose that my colleagues were tired of having children tell them what they think
Suppose the investigator referred to in Exercise 15.9 decided that instead of running one group and comparing it against μ0 = 5.8, she would run two groups (one with and one without lesions).She
As it turns out, a research assistant has just finished running the experiment described in Exercise 15.10 without having carried out any power calculations. He tried to run 20 subjects in each
Let’s modify Exercise 15.12 to have sample means of 25 and 28, with a pooled standard deviation of 8 and sample sizes of 20 and 20.a) What is the a priori power of this experiment?b) Run the t test
Diagram the answer to Exercise 15.13.Let’s modify Exercise 15.12 to have sample means of 25 and 28, with a pooled standard deviation of 8 and sample sizes of 20 and 20.a) What is the a priori power
Two graduate students have recently completed their dissertations. Each used a t test for two independent groups. One found a barely significant t using 10 subjects per group. The other found a
Assume we want to test a null hypothesis about a single mean at α = .05, one-tailed. Further assume that all necessary assumptions are met. Is there ever a case in which we are more likely to reject
If σ = 15, n = 25, and we are testing H0: μ = 100 versus H1: μ > 100, what value of the mean under H1 would result in power being equal to the probability of a Type II error?
Use G*Power or Piface (Lenth’s program) to calculate the power of the comparison of Thematic Apperception T scores from the parents of schizophrenic and normal subjects in Exercise 14.8.Exercise
Why would we ever want to calculate power after an experiment has been run, as we just did in Exercises 15.22 and 15.23?Exercise 15.22Calculate the power of the anorexia experiment in Section 14.1,
The Web page for this chapter’s R code includes code that will calculate power. Use that software to replicate the results you found in previous exercises.
What are two main assumptions behind the analysis of variance?
What does MSerror represent?
What does MSbetween represent?
Why is it called the analysis of variance if it is really a test on means?
What is the general rule for degrees of freedom?
Is the analysis of variance a one-tailed test or a two-tailed test?
What do we mean by “multiple comparison procedures”?
Do we need a significant overall F before running multiple comparison tests?
Why not just use plain old t tests instead of multiple comparison procedures?
Name three multiple comparison tests.
What does it mean when we say that a statistical test is “robust”?
The coefficient η2 is an _____ measure of effect size and is basically just the percentage of _____.
Another way to look at the Eysenck study mentioned in Exercise 16.1 is to compare four groups of participants. One group consisted of Younger participants who were presented the words to be recalled
Now we will expand on the analysis of Exercise 16.2.a) Run a one-way analysis of variance on treatments 1 and 3 combined (n = 20) versus treatments 2 and 4 combined. What question are you
Refer to Exercise 16.1. Assume that we collected additional data and had two more participants in the Younger group with scores of 13 and 15.a) Rerun the analysis of variance.b) Run an independent
Calculate η2 and ω2 for the data in Exercise 16.1 and write an interpretation.Exercise 16.1An important study in the memory literature is an old study by Eysenck (1974) in which he compared the
Calculate η2 and ω2 for the data in Exercise 16.2 and write an interpretation.Exercise 16.2Another way to look at the Eysenck study mentioned in Exercise 16.1 is to compare four groups of
Calculate η2 and ω2 for the data in Exercise 16.7, and interpret their meaning.Exercise 16.7Foa, Rothbaum, Riggs, and Murdock (1991) conducted a study evaluating four different types of therapy for
Use the R code on this chapter’s Web page to generate data that could lie behind exercise 16.7 and then run the analysis of variance.Exercise 16.7Foa, Rothbaum, Riggs, and Murdock (1991) conducted
How do the results of Exercise 16.9 compare with the results you obtained in Exercise 16.7?(They should agree, but not too closely.)Exercise 16.7Foa, Rothbaum, Riggs, and Murdock (1991) conducted a
What would happen if the sample sizes in Exercise 16.7 were twice as large as they were?Exercise 16.7Foa, Rothbaum, Riggs, and Murdock (1991) conducted a study evaluating four different types of
Use protected t tests for the data in Exercise 16.7 or 16.9 to clarify the meaning of the significant F.Exercise 16.7Foa, Rothbaum, Riggs, and Murdock (1991) conducted a study evaluating four
Use the R code in Section 16.3 to run the analysis of the data in Exercise 16.2.Exercise 16.2Another way to look at the Eysenck study mentioned in Exercise 16.1 is to compare four groups of
Perform a Bonferroni correction for the analysis of section 16.10. What comparisons make sense to you?
Calculate for the comparisons you made in Exercise 16.12 and interpret the meaning of each.Exercise 16.12Use protected t tests for the data in Exercise 16.7 or 16.9 to clarify the meaning of the
The data in Exercises 16.7 and 16.11 both produced a significant F. Do you have more or less faith in one of these effects? Why?Exercise 16.7Foa, Rothbaum, Riggs, and Murdock (1991) conducted a study
For the data in Appendix D, form three groups. (These data are available at www.uvm.edu/~dhowell/fundamentals9/DataFiles/Add.dat). Group 1 has ADDSC scores of 40 or below, Group 2 has ADDSC scores
Compute η2 and ω2 from the results in Exercise 16.17.Exercise 16.17For the data in Appendix D, form three groups. (These data are available at www.uvm.edu/~dhowell/fundamentals9/DataFiles/Add.dat).
Using the data in Exercise 16.2, calculate SSerror directly rather than by subtraction and show that this is the same answer you found in that exercise.Exercise 16.2Another way to look at the Eysenck
Use the Bonferroni correction for the data in Exercise 16.2 to compare the Younger/Low with the Older/Low group, and the Younger/High with the Older/High group.Exercise 16.2Another way to look at the
Use the Bonferroni correction for the data in Exercise 16.7 to compare the WL group with each of the other three groups. What would you conclude? How does this compare to the answer for Exercise
Calculate for the comparison of WL with SIT in Exercise 16.22 using the standard deviation of the Control group to standardize the difference.Exercise 16.22Use the Bonferroni correction for the
In the study referred to in Exercise 16.24, Spilich et al. (1992) also investigated performance on a cognitive task that required the participant to read a passage and then to recall it later.This
Use the Fisher LSD test to compare active smokers with nonsmokers and to compare the two groups of smokers on the data in Exercise 16.25 What do these data suggest about the advisability of smoking
The three experiments by Spilich et al. (1992) on the effects of smoking on performance find conflicting results. Can you suggest why the results are different?
Using the data from Exercise 16.29a) Calculate η2 and ω2.b) Why do the two estimates of the magnitude of effect in parta) differ?c) Calculate a measure of , using the most appropriate
Use R or SPSS to reproduce the analysis in Exercise 16.27.Exercise 16.27Spilich et al. (1992) ran a third experiment in which the three groups of smokers participated in a driving simulation video
Use Lenth’s Piface program or the one at www.statpages.org/pdfs.html to reproduce the probability values given in Exercise 16.31.Exercise 16.31Use R or SPSS to reproduce the analysis in Exercise
What is a factorial design?
What is a 2 × 3 factorial design?
What is a simple effect?
What do we mean by a cell in a factorial design?
How do we calculate the error sum of squares for a factorial design?
What should you say about main effects if there is a significant interaction?
When would you likely use a d-family measure of effect size in an analysis of variance?
What would an r-family measure of effect size tell us for a factorial design?
What is often the most important feature of a factorial analysis of variance?
To what does the symbol μ0 refer?
What do we mean by “matched samples”?
The major advantage of matched samples is that ____.
What is the usual null hypothesis with matched samples?
Give two advantages of a matched-samples study over a study with independent groups.
What does a value of = .95 tell you? a
In question “F,” what would we use in the denominator to calculate ? a
What is the difference in the standard deviation used to calculate and the standard deviation used to calculate a confidence interval? a
What is a carry-over effect?
In the study referred to in Exercise 13.1, what, if anything, does your answer to that questiontell us about whether couples are sexually compatible? What do we know from this analysis,and what
For the data in Exercise 13.1, create a scatterplot and calculate the correlation between husband’sand wife’s sexual satisfaction. How does this amplify what we have learned from theanalysis in
Use techniques developed in Chapter 12 and this chapter to construct 95% confidence limitson the true mean difference between the Sexual Satisfaction scores in Exercise 13.1.Exercise 13.1Hout,
Some would object that the data in Exercise 13.1 are clearly discrete, if not ordinal, as definedin Chapter 2, and that it is inappropriate to run a t test on them. Can you think what mightbe a
Why would you use a paired t test in Exercise 13.6?Exercise 13.6Hoaglin, Mosteller, and Tukey (1983) present data on blood levels of beta-endorphin as afunction of stress. They took beta-endorphin
Create a scatterplot of the data in Exercise 13.6, and compute the correlation between the twosets of scores. What does this say that is relevant to the answer to Exercise 13.7?Exercise 13.7Why would
We always need to look closely at our data. Sometimes we find things that are hard to explain.Look closely at the data in Exercise 13.6; what attracts your attention?Exercise 13.6Hoaglin, Mosteller,
Compute a measure of effect size for the data in Exercise 13.6, and tell what this measureindicates.Exercise 13.6Hoaglin, Mosteller, and Tukey (1983) present data on blood levels of beta-endorphin as
Assume that the mean and the standard deviation of the difference scores in Exercise 13.6would remain the same if we added more subjects. How many subjects would we need toobtain a t that is
Modify the data in Exercise 13.6 by shifting the entries in the “12 hour” column so as to increasethe relationship between the two variables. Run a t test on the modified data and notice
Using your answer to Exercise 13.14 and your knowledge about correlation, how would youexpect the degree of correlation between two variables (sets of data) to affect the magnitude ofthe t test
Whether or not you found a significant difference in Exercise 13.13, Vul and Pashler did. Butare first guesses better than the average of the two?Exercise 13.13Assume that the mean and the standard
In the anorexia example in Section 13.2 I subtracted the After scores from the Before scores.What would have happened if I had done that the other way around?
Many mothers experience a sense of depression shortly after the birth of a child, known aspostpartum depression (PPD). Design a study to examine PPD and tell how you would estimatethe mean increase
We have not discussed confidence limits on effect sizes, but Ken Kelly and Keke Lai, at NotreDame, created an R library named MBESS to calculate such limits. Using the data in Table13.1, compute
Give two reasons why we would run an experiment with independent groups of scores.
What is the difference between N and n?
What do we mean by “pooling variances”?
What is meant by the assumption of “homogeneity of variance”?
What do we mean when we say that two effects are “confounded”?
What do we mean by a “bidirectional” hypothesis?
How does the calculation of confidence limits on the difference between two meansdiffer from the calculation when we have one mean?
What are error bars?
In Exercise 13.1 we had paired data because we had a response from both the husband and the wife within a married couple. Suppose that instead of using married couples we just took a large group of

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