Question

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EXERCISES 101 About the Data The Web shopping data in this chapter (and Chapter 3) kitchen preferences Consump- in the United States.) The data for derived from surveys reported by ComScore, a are a subset of the Residential Energy (RECS), performed by the Department of of attitudes toward file sharing are firm that monitors the Web-browsing habits of a tion Survey on airline arrivals in the 4M example of tics. (From the main page, follow the links to data that rounded the counts to simplify the Simpson's x are from the Bureau of Transportation Statis- is from a story in the Daily Pennsylvanian, the stu- the University of Pennsylvania. We dent newspaper a ceing association ariable offers summarize information about various types of travel example. ound in a an. EXERCISES that defin k Cramer's V are sociationare Mix and Match Match the description of the item in the first column to the term in the second column. 1. Table of cross-classiied counts 2. Counts cases that match values of two categorical variables 3. Shown in the bar chart of a categorical variable 4. Shown in a stacked bar chart 5. Measure of association that grows with increased sample size 6. Measure of association that lies between 0 and 1 7. Happens if the conditional distribution matches the marginal distribution 8. Identified when percentages within a row differ from marginal percentages 9. Produced by a variable lurking behind a table 90 b. mosaic plot associated d. Simpson's paradox e. marginal distribution f. cell g. conditional distribution h. Cramer's V i. not associated j. contingency table le to stacked 10. Like a stacked bar chart but respecting the area principle luces Simp- that Simp- er all. 19. If the categorical variable that identifies the supervis True/False ing manager is associated with the categorical vari- associa ared and Mark each statement True or False. If you believe that a able that indicates a problem with processing orders, then the manager is causing the problems. 20. A small chi-squared statistic suggests that a lurking statement is false, briefly say why you think it is false 11. We can fill in the cells of the contingency table from nal counts if the two categorical variables variable conceals the association between two cat- are not associated ables by comparing their bar charts. each row of a contingency table (row percentages) egorical variables. 12. We can see association between two categorical vari- 21. If the percentage of female job candidates who are summa formula hired is larger than the percentage of male candidates who are hired, then there is association between the cat- 13. The percentages of cases in the first column within are the same if the variables are not associated. 14. A large chi-squared tells us that there is strong asso- egorical variables Sex (male, female) and Hire (yes, no). 22. If the percentage of defective items produced by a manufacturing process is about the same on Monday, Tuesday, Wednesday, Thursday, and Friday, then the day of the week is associated with defective items. 15. The value of chi-squared depends on the number of 16. Cramer's V is 0 if the categorical variables are not 17. The value of chi-squared depends on which variable ciation between two categorical variables. cases in a contingency table. associated. Think About It 23. This table shows counts from a consumer satisfaction defines the rows and which defines the columns of the contingency table. survey of 2,000 customers who called a credit card company to dispute a charge. One thousand custom- ers were retired, and the remaining were employed. (a) What would it mean to find association between 18. If variable X is associated with variable Y, then Y is nma- these variables? caused by X

Answer 1

11) We can fill in the cells of contingency table from the marginal counts if the two categorical variables are not associated.

TRUE. If the percentages in the table match those in the margins, there’s little association. The counts might not match perfectly due to rounding, but they should be very close. Thus we can fill in the cells of contingency table from the marginal counts if the variables are not associated because the proportions will match.

12) We can see association between two categorical variables by comparing their bar charts.

FALSE. We have to see the cells of the table, not just the marginal counts. Bar charts show only the marginal distribution, not the presence of association.

13) The percentage of cases in the first column within each row of a contingency table are the same if the variables are not associated.

TRUE. That if the conditional proportion for one categorical variable categories are the same for each category of other categorical variable, then there is no association between two variables.

14) A large chi squared tells us that there is strong association between two categorical variables.

FALSE. Chi-square might be large just because of the size of the table and the number of observations.

15) The value of chi square depends on the number of observations in the contingency table .

TRUE. Because chi square statistic value is more sensitive to sample size. That is, as the number of observations increases the value of chi square statistic will increase.

16) Cramer's V is 0 if the categorical variables are not associated.

TRUE. Because when the variables are not associated the proportions are the same therefore, the difference will be 0 and therefore, chi square value will be 0 and Cramer’s V will also be 0.

17)  The value of chi square depends on which variables define the rows and which define the columns of the contingency table.

FALSE. Because even if we interchange the rows and columns the chi square value will remain the same.

18) If variable X is associated with variable Y, then Y is caused by X.

FALSE. Association does not imply causation.

19) If the categorical variable that identifies the supervising manager is associated with the categorical variable that indicates a problem with processing orders, then the manager is causing the problem.

FALSE. Association is not the same as cause and effect. We cannot interpret association as causation because of the possible presence of a lurking variable. Some managers may operate under very different conditions.

20) A small chi square statistic suggests that a lurking variable conceals the association between two categorical variables.

FALSE. You can only guess the presence of a lurking variable if you know the context of the problem and suspect that the initial table hides a lurking variable.

21) If the percentage of female job candidates who are hired is larger than the percentage of male candidates who are hired, then there is association between categorical variables sex [Male, Female] and Hire [Yes, No].

TRUE.

22) If the percentage of defective items produced by manufacturing process is about the same on Monday, Tuesday, Wednesday, Thursday and Friday, then the day of the week is associated with the defective items.

FALSE. If the proportions are same then there is no association. Thus day of the week is not associated with the defective items.