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statistical sampling to auditing

Questions and Answers of Statistical Sampling To Auditing

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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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?
The Thematic Apperception Test presents subjects with ambiguous pictures and asks them to tell a story about them. These stories can be scored in any number of ways. Werner, Stabenau, and Pollin
What is the role of random assignment in the Everitt’s anorexia study referred to in Exercise==7.31, and under what conditions might we find it difficult to carry out random assignment?
Why isn’t the difference between the results in 7.34 and 7.19 greater than it is?
Run the appropriate t test on the data in 7.19 assuming that the observations are independent.What would you conclude?
In Exercise 7.19 we saw pairs of observations on sexual satisfaction for husbands and wives.Suppose that those data had actually come from unrelated males and females, such that the data are no
Calculate the confidence interval on m1 2 m2 and d for the data in Exercise 7.31. If available, use the software mentioned earlier to calculate confidence limits on d.
In Exercise 7.25, data from Everitt showed that girls receiving cognitive behavior therapy gained weight over the course of the therapy. However, it is possible they just gained weight because they
Many mothers experience a sense of depression shortly after the birth of a child. Design a study to examine postpartum depression and, from material in this chapter, tell how you would estimate the
In the study referred to in Exercise 7.13, Katz et al. (1990) compared the performance on SAT items of a group of 17 students who were answering questions about a passage after having read the
For the control condition of the experiment in Exercise 7.25 the beginning and 10-week means were 4.32 and 4.61 with standard deviations of 0.98 and 1.13, respectively. The sample size was 130. Using
Another way to investigate the effectiveness of the intervention described in Exercise 7.25 would be to note that the mean quality-of-life score before the intervention was 4.47 with a standard
In Exercise 7.25 calculate a confidence interval for the difference in group means. Then calculate a d-family measure of effect size for that difference.
Sullivan and Bybee (1999) reported on an intervention program for women with abusive partners. The study involved a 10-week intervention program and a three-year follow-up, and used an experimental
Give an example of an experiment in which using related samples would be ill-advised because taking one measurement might influence another measurement.
Some would object that the data in Exercise 7.19 are clearly discrete, though ordinal, and that it is inappropriate to run a t test on them. Can you think what might be a counter argument?(This is
Construct 95% confidence limits on the true mean difference between the Sexual Satisfaction scores in Exercise 7.19, and interpret them with respect to the data.
Using any available software, create a scatterplot and calculate the correlation between husband’s and wife’s sexual satisfaction in Exercise 7.19. How does this amplify what we have learned from
In the study referred to in Exercise 7.19, what, if anything does your answer to that question tell us about whether couples are sexually compatible? What do we know from this analysis, and what
Hout, Duncan, and Sobel (1987) reported on the relative sexual satisfaction of married couples.They asked each member of 91 married couples to rate the degree to which they agreed with “Sex is fun
Calculate an effect size for the data in Exercise 7.16.
Construct 95% confidence limits on the true mean difference between endorphin levels at the two times described in Exercise 7.16.
Hoaglin, Mosteller, and Tukey (1983) present data on blood levels of beta-endorphin as a function of stress. They took beta-endorphin levels for 19 patients 12 hours before surgery, and again 10
Calculate the 95% confidence limits for m for the data in Exercise 7.14. Are these limits consistent with your conclusion in Exercise 7.14?
Compas and others (1994) were surprised to find that young children under stress actually report fewer symptoms of anxiety and depression than we would expect. But they also noticed that their scores
Katz, Lautenschlager, Blackburn, and Harris (1990) examined the performance of 28 students who answered multiple choice items on the SAT without having read the passages to which the items referred.
Compute 95% confidence limits on the weight gain in Exercise 7.11.
Everitt, in Hand et al., 1994, reported on several different therapies as treatments for anorexia.There were 29 girls in a cognitive-behavior therapy condition, and they were weighed before and after
Compute 95% confidence limits on m for the data in Exercise 7.8.
The over- and underestimation of one’s performance is partly a function of the fact that if you are near the bottom you have less room to underestimate your performance than to overestimate it. The
In what way would the result in Exercise 7.2 differ if you had drawn more samples of size 5?==7.5. In what way would the result in Exercise 7.2 differ if you had drawn 50 samples of size 15?==7.6.
Compare the means and the standard deviations for the distribution of digits in Exercise 7.1 and the sampling distribution of the mean in Exercise 7.2.a. What would the Central Limit Theorem lead you
I drew 50 samples of 5 scores each from the same population that the data in Exercise 7.1 came from, and calculated the mean of each sample. The means are shown below. Plot the distribution of these
The following numbers represent 100 random numbers drawn from a rectangular population with a mean of 4.5 and a standard deviation of .2.7. Plot the distribution of these digits.6 4 8 7 8 7 0 8 2 8 5
In the text I calculated odds ratios for the data in Table 6.11. Do the same for relative risk.
Appleton, French, and Vanderpump (1996) present data that would appear to show that smoking is good for you. They assessed smoking behavior in the early 1970s and then looked at survival data 20
The State of Maine collected data on seat belt use and highway fatalities in 1996. (Full data are available at http://maine.gov/dps/bhs/crash-data/stats/seatbelts.html)Psychologists often study how
Fidalgo (2005) presented data on the relationship between bullying in the work force (Yes/No) and gender (Male/Female) of the bully. He further broke the data down by job level.The data are given
The following data come from Ramsey and Shafer (1996) but were originally collected in conjunction with the trial of McClesky v. Zant in 1998. In that trial the defendant’s lawyers tried to
In the previous question we were concerned with whether husbands and wives rate their degree of sexual fun congruently (i.e., to the same degree). But suppose that women have different cut points on
Hout, Duncan, and Sobel (1987) reported data on the relative sexual satisfaction of married couples. They asked each member of 91 married couples to rate the degree to which they agreed with “Sex
The Zuckerman et al. paper referred to in the previous question hypothesized that faculty were less accurate than students because they have a tendency to give negative responses to such questions.
Zuckerman, Hodgins, Zuckerman, and Rosenthal (1993) surveyed over 500 people and asked a number of questions on statistical issues. In one question a reviewer warned a researcher that she had a high
When we look at the variables in Mireault’s data, we will want to be sure that there are not systematic differences of which we are ignorant. For example, if we found that the gender of the parent

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