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Statistical Methods For Psychology 8th Edition David C. Howell - Solutions
Calculate h2 and v2 for the data in Exercise 11.3.
Calculate h2 and v2 for the data in Exercise 11.2. Would you assume a fixed or a random model?
Refer to Exercise 11.2. Suppose that we collected additional data and had two more subjects in the Younger group, with scores of 13 and 15.a. Rerun the analysis of variance.b. Run an independent groups t test without pooling the variances.c. Run an independent groups t test after pooling the
Refer to Exercise 11.3. Now run an analysis of variance on treatments 1 and 2 combined compared with treatments 3 and 4 combined. What hypothesis are we testing?
Another way of looking at the data from Eysenck’s (1974) study is to compare four groups of subjects. One group consisted of Younger subjects who were presented the words to be recalled in a condition that elicited a Low level of processing. A second group involved Younger subjects who were given
Another aspect of the study by Eysenck (1974), referred to in Exercise 11.1, compared Younger and Older subjects on their ability to recall material in the face of instructions telling them that they would be asked to memorize the material for later recall—the Intentional group. (Presumably this
Eysenck (1974) ran a study in which participants were required to recall a list of words. The conditions varied in terms of whether subjects simply counted the number of letters in a word, thought of a rhyming word, thought of an appropriate adjective, created images of the word, or was told to
Rosenthal and others (cited earlier) have argued that small effects, as indexed by a small r2, for example, can be important in certain situations. We would probably all agree that small effects could be trivial in other situations.a. Can an effect that is not statistically significant ever be
Repeat the analysis shown in Exercise 10.19, but this time cross-tabulate ClinCase against Gender.a. Compare this answer with the results of Exercise 10.18.b. How does this analysis differ from the one in Exercise 10.18 on roughly the same question?
In Exercise 7.48 using Mireault.dat, we compared the responses of students who had lost a parent and students who had not lost a parent in terms of their responses on the Global Symptom Index T score (GSIT), among other variables. An alternative analysis would be to use a clinically meaningful
Using Mireault’s data on this book’s Web site (Mireault.dat), calculate the point-biserial correlation between Gender and the Depression T score. Compare the relevant aspects of this question to the results you obtained in Exercise 7.46. (See “The Relationship Between rpb and t” in Section
On page 312 I noted that Rosenthal and Rubin showed that an r2 of .1024 actually represented a pretty impressive effect. They demonstrated that this would correspond to a x2 of 20.48, and with 100 subjects in each of two groups, the 2 3 2 contingency table would have a 34:66 split for one row and a
Assume in Exercise 10.14 that there were five entering clinical students. They produced the following data:Student 1: 1 4 2 6 5 3 9 10 7 8 Student 2: 4 3 2 5 7 1 10 8 6 9 Student 3: 1 5 2 6 4 3 8 10 7 9 Student 4: 2 5 1 7 4 3 10 8 6 9 Student 5: 2 5 1 4 6 3 9 7 8 10 Calculate Kendall’s W and rS
Rerun the analysis on Exercise 10.14 using Kendall’s t.
In a study of diagnostic processes, entering clinical graduate students are shown a 20-minute videotape of children’s behavior and asked to rank order 10 behavioral events on the tape in the order of the importance each has for a behavioral assessment (1 5 most important). The data are then
For the data in Exercise 10.12,a. Compute Kendall’s t.b. Test t for significance.
An investigator wants to arrange the 15 items on her scale of language impairment on the basis of the order in which language skills appear in development. Not being entirely confident that she has selected the correct ordering of skills, she asks another professional to rank the items from 1 to 15
An investigator is interested in the relationship between alcoholism and a childhood history of attention deficit disorder (ADD). He has collected the following data, where a 1 represents the presence of the relevant problem.ADD: 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 Alcoholism: 0 1 0 0 0 1 0 0 0 1 1 0 0
Visualize the data in Exercise 10.9 as fitting into a contingency table.a. Compute the chi-square on this table.b. Show the relationship between chi-square and w.
Some people think that they do their best work in the morning, whereas others claim that they do their best work at night. We have dichotomized 20 office workers into morning or evening people (0 5 morning, 1 5 evening) and have obtained independent estimates of the 22046
The distinction between confidence intervals and prediction intervals in regression is often difficult to grasp. Do a Google search to find a clear explanation of the distinction.
Going back to the example on popularity and academic achievement, run the appropriate test to compare the correlations in males and females between Perceived Popularity and Sociometric Popularity.
In 1801 a celestial object named Ceres was discovered by Giuseppi Piazzi at 2.767 astronomical units from the sun. It was called a dwarf planet, but those are now plutoids. If it were classed as a planet, how would this fit with the other planets we know as shown in Table 9.7?
In 2005 an object was discovered out beyond Pluto that was (unofficially) named Xena and now is called Eris. It is larger than Pluto but is not considered a planet—the new title is “plutoid.”It is 96.7 astronomical units from the sun. How does such an object fit with the data in Table 9.7?
In a recent e-mail query, someone asked about how they should compare two air pollution monitors that sit side-by-side and collect data all day. They had the average reading per monitor for each of 50 days and wanted to compare the two monitors; their first thought was to run a t test between the
In Chapter 2 I presented data on the speed of deciding whether a briefly presented digit was part of a comparison set and gave data from trials on which the comparison set had contained one, three, or five digits. Eventually, I would like to compare the three conditions(using only the data from
The slope (b) used to predict the weights of males from their heights is greater than the slope for females. Is this significant, and what would it mean if it were?
Given a male and a female student who are both 5960, how much would they be expected to differ in weight? (Hint: Calculate a predicted weight for each of them using the regression equation specific to their gender.)
Use your scatterplot of the data for students of your own gender and observe the size of the residuals. (Hint: You can see the residuals in the vertical distance of points from the line.)What is the largest residual for your scatterplot?
The following data are the actual heights and weights, referred to in this chapter, of female college students.a. Make a scatterplot of the data.b. Calculate the regression coefficients for these data. Interpret the slope and the intercept.c. What is the correlation coefficient for these data? Is
The following data represent the actual heights and weights referred to earlier for male college students.a. Make a scatterplot of the data.b. Calculate the regression equation of weight predicted from height for these data. Interpret the slope and the intercept.c. What is the correlation
One of the assumptions lying behind our use of regression is the assumption of homogeneity of variance in arrays. One way to examine the data for violations of this assumption is to calculate predicted values of Y and the corresponding residuals (Y – Y ˆ ). If you plot the residuals against the
Using the data referred to in Exercise 9.28,a. calculate the correlations among all of the Brief Symptom Inventory subscales. (Hint:Virtually all statistical programs are able to calculate these correlations in one statement.You don’t have to calculate each one individually.)b. What does the
Using the data from Mireault and Bond (1992) in the file Mireault.dat, at http://www.uvm.edu/~dhowell/methods8/DataFiles/DataSets.html, is there a relationship between how well a student performs in college (as assessed by GPA) and that student’s psychological symptoms(as assessed by GSIT)?
Moore and McCabe (1989) found some interesting data on the consumption of alcohol and tobacco that illustrate an important statistical concept. Their data, taken from the Family Expenditure Survey of the British Department of Employment, follow. The dependent variables are the average weekly
Make up your own example along the lines of the “smoking versus life expectancy” example given on pp. 270–271 to illustrate the relationship between r2 and accountable variation.
What conclusions can you draw from the difference between the correlations in Exercises 9.23 and 9.24?
Katz et al. replicated their experiment using subjects whose SAT Verbal scores showed considerably more within-group variance than those in the first study. In this case the correlation for the group that read the passage was .88 (N 5 52), whereas for the nonreading group it was .72 (N 5 74). Were
In the study by Katz, Lautenschlager, Blackburn, and Harris (1990) used in this chapter and in Exercises 7.13 and 7.29, we saw that students who were answering reading comprehension questions on the SAT without first reading the passages performed at better-thanchance levels. This does not
and 9.21. She obtained the data for all 50 states on several variables associated with school performance, including expenditures for education, SAT performance, percentage of students taking the SAT, and other variables. We will look more extensively at these data later, but the following table
Guber (1999) actually assembled the data to address the basic question referred to in Exercises
In Exercise 9.20 how many districts would you need for power 5 .80?
You want to demonstrate a relationship between the amount of money school districts spend on education and the performance of students on a standardized test such as the SAT. You are interested in finding such a correlation only if the true correlation is at least .40. What are your chances of
The data file named Galton.dat on this book’s Web site contains Galton’s actual data on heights of parents and children discussed under the heading of “regression to the mean.”In these data Galton multiplied mothers’ and daughters’ heights by 1.08 to give them the same mean as males’
In 1886, Sir Francis Galton, an English scientist, spoke about “regression toward mediocrity,”which we more charitably refer to today as regression toward the mean. The basic principle is that those people at the ends of any continuum (e.g., height, IQ, or musical ability) tend to have children
Calculate an equation for the 95% confidence interval in Y^for predicting psychological symptoms for new cases—you can overlay the confidence limits on Figure 9.2.
The mean stress score for the data in Table 9.3 was 21.467. What would your prediction for log(symptoms) be for someone who had that stress score? How does this compare to Y?
Using the information in Table 9.2 and the computed coefficients, predict the score for log(symptoms) for a stress score of 8.
How many infants would be required for power to be .80 in Exercise 9.13?
An important developmental question concerns the relationship between severity of cerebral hemorrhage in low-birthweight infants and cognitive deficit in the same children at age 5 years. Suppose we expect a correlation of .20 and are planning to use 25 infants. How much power does this study have?
One way to get around the problem you see in Exercise 9.11 is to convert the incidence of Down’s syndrome to ranked data. Replot the data using ranked incidence and calculate the correlation. This is a Spearman’s correlation, as we will see in the next chapter.
Why would you not feel comfortable computing a Pearson correlation on the data in Exercise 9.10?
Down’s syndrome is another problem that psychologists deal with. It has been proposed that mothers who give birth at older ages are more likely to have a child with Down’s syndrome.Plot the data below relating age to incidence. The data were taken from Geyer (1991).
Infant mortality is a very serious problem to society. Why would psychologists be interested in this problem any more than people in other professions?
From the previous exercises do you think that we are able to conclude that low income causes infant mortality?
Two predictors of infant mortality seem to be significant. If you could find a way to use both of them as predictors simultaneously, what do you think you would find?
In Exercise 9.1 the percentage of mothers over 40 does not appear to be important, and yet it is a risk factor in other societies. Why do you think that this might be?
What can we conclude from the data on infant mortality?
What are the strongest predictors of infant mortality in Exercise 9.2?
Using the table in Appendix t, how large a correlation would you need for the relationships shown in Exercise 9.2 to be significant?
Calculate the correlations among all numeric variables in Exercise 9.1 using SPSS.
In Sub-Saharan Africa, more than half of mothers lose at least one child before the child’s first birthday. Below are data on 36 countries in the region, giving country, infant mortality, per capita income (in U.S. dollars), percentage of births to mothers under 20, percentage of births to
Create an example in which a difference is just barely statistically significant at a 5 .05.(Hint: Find the critical value for t, invent values for m1 and m2 and n1 and n2, and then solve for the required value of s.) Now calculate the retrospective power of this experiment.
Why do you suppose that Exercises 8.21 and 8.22 belong in a statistics text?
In the modification of Aronson’s study to use a matched-sample t test, I always gave the Control condition first, followed by the Threat condition in the next week.a. Why would this be a better approach than randomizing the order of conditions?b. If I give exactly the same test each week, there
In the hypothetical study based on Aronson’s work on stereotype threat with two independent groups, I could have all male students in a given lab section take the test under the same condition. Then male students in another lab could take the test under the other condition.a. What is wrong with
Prentice and Miller (1992) presented an interesting argument that while most students do their best to increase the effect size of whatever they are studying (e.g., by maximizing the differences between groups), some research focuses on minimizing the effect and still finding a difference. (For
If s 5 15, n 5 25, and we are testing H0 : m0 5 100 versus H1 : m0 . 100, what value of the mean under H1 would result in power being equal to the probability of a Type II error?(Hint: Try sketching the two distributions; which areas are you trying to equate?)
Assume that we want to test a null hypothesis about a single mean at a 5 .05, one-tailed.Further assume that all necessary assumptions are met. Could there be a case in which we would be more likely to reject a true H0 than to reject a false one? (In other words, can power ever be less than a?)
Let’s extend Aronson’s study (discussed in Section 8.5) to include women (who, unfortunately, often don’t have as strong an investment in their skills in mathematics as men.They probably also are not as tied up in doing better than someone else). For women we expect means of 8.5 and 8.0 for
Use G*Power or similar software to reproduce the results found in Section 8.5.
A beleaguered PhD candidate has the impression that he must find significant results if he wants to defend his dissertation successfully. He wants to show a difference in social awareness, as measured by his own scale, between a normal group and a group of ex-delinquents.He has a problem, however.
Make up a simple two-group example to demonstrate that for a total of 30 subjects, power increases as the sample sizes become more nearly equal.
Draw a diagram (analogous to Figure 8.2) to defend your answer to Exercise 8.12.
Two graduate students recently completed their dissertations. Each used a t test for two independent groups. One found a significant t using 10 subjects per group. The other found a significant t of the same magnitude using 45 subjects per group. Which result impresses you more?
Run the t test on the original data in Exercise 8.10. What, if anything, does your answer to this question indicate about your answer to Exercise 8.10?
We have just conducted a study comparing cognitive development of low- and normal-birthweight babies who have reached 1 year of age. Using a scale we devised, we found that the sample means of the two groups were 25 and 30, respectively, with a pooled standard deviation of 8. Assume that we wish to
A research assistant ran the experiment described in Exercise 8.8 without first carrying out any power calculations. He tried to run 20 subjects in each group, but he accidentally tipped over a rack of cages and had to void 5 subjects in the experimental group. What is the power of this experiment?
Suppose that the laboratory referred to in Exercise 8.7 decided not to run one group and compare it against m0 5 5.8, but instead to run two groups (one with and one without lesions). They still expect the same degree of difference.a. How many subjects do they need (overall) if they are to have
A physiological psychology laboratory has been studying avoidance behavior in rabbits for several years and has published numerous papers on the topic. It is clear from this research that the mean response latency for a particular task is 5.8 seconds with a standard deviation of 2 seconds (based on
Assume that a third investigator ran both conditions described in Exercises 8.2 and 8.5 and wanted to know the power of the combined experiment to find a difference between the two experimental manipulations.a. What is the effect size in question?b. What is the value of d if the size of his sample
A second investigator thinks that she can show that a quite different manipulation can raise the mean influence score from 520 to 550.a. What is the effect size in question?b. What is the value of d if the size of her sample is 100?c. What is the power of the test?8.5 Diagram the situation
In Exercise 8.1 what sample sizes would be needed to raise power to .70, .80, and .90?
Diagram the situation described in Exercise 8.1 along the lines of Figure 8.1.
A large body of literature on the effect of peer pressure has shown that the mean influence score for a scale of peer pressure is 520 with a standard deviation of 80. An investigator would like to show that a minor change in conditions will produce scores with a mean of only 500, and he plans to
Write a short paragraph containing the information necessary to describe the results of the experiment discussed in Exercise 7.31. This should be an abbreviated version of what you would write in a research article.
In Chapter 6 (Exercise 6.34) we examined data presented by Hout et al., on the sexual satisfaction of married couples. We did so by setting up a contingency table and computing x2 on that table. We looked at those data again in a different way in Exercise 7.19, where we ran a t-test comparing the
Present meaningful effect sizes estimate(s) for the two independent group data in Exercise 7.31.
Present meaningful effect sizes estimate(s) for the matched pairs data in Exercise 7.25.
Now run separate t tests to compare Mireault’s Group 1 versus Group 2, Group 1 versus Group 3, and Group 2 versus Group 3 on the Global Symptom Index. (This is not a good way to compare the three group means, but it is being done here because it leads to more appropriate analyses in Chapter 12.)
It is commonly reported that women show more symptoms of anxiety and depression than men. Would the data from Mireault’s study support this hypothesis?
Research on clinical samples (i.e., people referred for diagnosis or treatment) has suggested that children who experience the death of a parent may be at risk for developing depression or anxiety in adulthood. Mireault and Bond (1992) collected data on 140 college students who had experienced the
I stated earlier that Levene’s test consists of calculating the absolute (or squared) differences between individual observations and their group’s mean, and then running a t test on those differences. By using any computer software it is simple to calculate those absolute and squared
What does a comparison of Exercises 7.42 and 7.43 show you?
A second investigator repeated the experiment described in Exercise 7.42 and obtained the same results. However, she thought that it would be more appropriate to record the data in terms of minutes per problem (e.g., 4 problems in 10 minutes 5 10/4 5 2.5 minutes/problem).Thus, her data were:Innate
An experimenter examining decision making asked 10 children to solve as many problems as they could in 10 minutes. One group (5 subjects) was told that this was a test of their innate problem-solving ability; a second group (5 subjects) was told that this was just a timefilling task. The data
Calculate 95% confidence limits on m1 – m2 and d for the data in Exercise 7.40.
Much has been made of the concept of experimenter bias, which refers to the fact that even the most conscientious experimenters tend to collect data that come out in the desired direction(they see what they want to see). Suppose we use students as experimenters. All the experimenters are told that
In Exercise 7.37 a significant difference might lead someone to suggest that poor parent-child relationships are the cause of schizophrenia. Why might this be a troublesome conclusion?
In Exercise 7.37 why might it be smart to look at the variances of the two groups?
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