CHAPTER 1: INTRODUCTION AND OVERVIEW

Solutions to problems for "Categorical Data Analysis for the Behavioral and Social Sciences" by R. Azen & C. M. Walker

CHAPTER 1: INTRODUCTION AND OVERVIEW

1

1.1

• Interval

b . Ordinal

• Ordinal

1.2

• Interval

b . Nominal

• Ratio

1.3 Answers can vary; scales should be described and match the level of measurement given in the

answers. For example:

• Dependent Variable = Mathematics Achievement, measured by a mathematics achievement test

(interval measurement); Independent Variable = Sex, measured by one demographic question (nominal measurement) b . Dependent Variable = Satisfaction with Life, measured by a multiple item survey (interval measurement); Independent Variable = Relationship Status, measured by one dichotomous demographic question (nominal measurement)

• Dependent Variable = Body Image, measured by a multiple item survey (interval measurement);

Independent Variable = Sex, measured by one demographic question (nominal measurement) d . Dependent Variable = Level of Education, measured by number of years attended school (ratio measurement); Independent Variable = Religious Affiliation, measured by one demographic survey item (nominal measurement) 1.4 Answers can vary; scales should be described and match the level of measurement given in the

answer. For example:

• Dependent Variable = Weight, measured in

kilograms (ratio measurement); Independent Variable = Country, measured by demographic question (nominal measurement) b . Dependent Variable = Cholesterol level, as measured by a blood test (ratio measurement); Independent Variable = Sex, measured by one demographic question (nominal measurement)

• Dependent Variable = Political Affiliation, measured by one multiple-category Likert survey item

that ranges from Strong Democrat to Strong Republican (ordinal measurement); Independent Variable = Sex, measured by one demographic question (nominal measurement) d . Dependent Variable = Grades in High School, measured by GPA (ratio measurement); Independent Variable = Amount of sleep, measured by a survey item that asks respondents the number of hours they sleep each night (ratio measurement) 1 Note that for many of these problems there may be more than one correct answer regarding level of measurement.The answers depend on and should be evaluated by the students' explanation of how the variables will be measured.Categorical Data Analysis for the Behavioral and Social Sciences, 1e Razia Azen, Cindy Walker (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) 1 / 4

1.5 Answers can vary; scales should be described and match the level of measurement given in the

answer. For example:

• The dependent variable in this scenario is presidential choice, which is a nominal variable. The

independent variable in this scenario is income. If income is measured by the gross annual income, then it would be a ratio variable. However, if income is measured by a survey item that categorizes income (e.g., < 9,999; $10,000 to $29, 999, $30,000 to $49,999, etc.) then it is an ordinal variable. Regardless, since the dependent variable is a nominal variable, procedures for analyzing categorical data are needed.

• The dependent variable in this scenario is presidential choice, which is a nominal variable. The

independent variable in this scenario is income. If income is measured by gross annual income, then it would be a ratio variable and procedures for analyzing categorical data are not needed.However, if income is measured by a survey item that categorizes income (e.g., < 9,999; $10,000 to $29, 999, $30,000 to $49,999, etc.) then it is an ordinal variable and procedures for analyzing categorical data are needed.

• The dependent variable in this scenario is fat content in diet. This is best measured by having

participants track their meals for a week and then counting up the grams of fat consumed on an average day, which would make it a ratio variable. The independent variable is whether or not one has had a heart attack, which is a nominal variable. Since the dependent variable is a ratio variable, procedures for analyzing categorical data are not needed.

• The dependent variable whether or not one has had a heart attack, which is a nominal variable.

The independent variable in fat content in diet, which can be measured as described in 1.5(c) and is a ratio variable. Since the dependent variable is a nominal variable, procedures for analyzing categorical data are needed.

1.6 Answers can vary; scales should be described and match the level of measurement given in the

answer. For example:

• The dependent variable in this scenario is whether or not one graduated from high school, which

is a dichotomous nominal variable. The independent variable in this scenario is grade point average, which is a ratio variable. Since the dependent variable is a nominal variable, procedures for analyzing categorical data are needed.

• The dependent variable in this scenario is grade point average, which is a ratio variable.

Therefore, procedures for analyzing categorical data are not needed.

• The dependent variable in this scenario is annual income. The independent variable is whether or

not a respondent attended college, which is a nominal (dichotomous) variable. If income is measured by gross annual income, then it would be a ratio variable and procedures for analyzing categorical data are not needed. However, if income is measured by a survey item that categorizes income (e.g., < 9,999; $10,000 to $29, 999, $30,000 to $49,999, etc.) then it is an ordinal variable and procedures for analyzing categorical data are needed.

• The dependent variable in this scenario is whether or not one attended college, which is a nominal

(dichotomous) variable. Therefore, regardless of the manner in which income is measured, procedures for analyzing categorical data are needed.

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1.7 Answers can vary; scales should be described and match the level of measurement given in the

answer. For example:

• The dependent variable in this scenario is reading proficiency, which is typically measured as an

ordinal variable (for example, when reading proficiency is differentiated into four categories such as minimal, basic, proficient, and advanced, as is commonly done). Thus, procedures for analyzing categorical data are needed.

• The dependent variable in this scenario is income and the independent variable is gender. If

income is measured by gross annual income, then it would be a ratio variable and procedures for analyzing categorical data are not needed. In this case an ANOVA analysis could be used to determine if the average annual income differs for males and females. However, if income is measured by a survey item that categorizes income (e.g., < 9,999; $10,000 to $29, 999, $30,000 to $49,999, etc.) then it is an ordinal variable and procedures for analyzing categorical data are needed.

• The dependent variable in this scenario is once again income. The independent variable is level

of education. Both variables can be measured as either categorical or continuous variables. The following table provides the correct analytical procedure for all four possible combinations: Measurement of Income Measurement of Education Analytical Procedure Ratio Ratio Regression Ratio Ordinal ANOVA Ordinal Ratio Categorical Procedure Ordinal Ordinal Categorical Procedure

• In this scenario both variables are categorical and thus procedures for analyzing categorical data

are needed.

1.8 Answers will vary.

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Solutions to problems for "Categorical Data Analysis for the Behavioral and Social Sciences" by R. Azen & C. M. Walker

CHAPTER 2: PROBABILITY DISTRIBUTIONS

2.1 This probability can be determined using the hypergeometric distribution:

N = 25, n = 5, m = 12, k = 0

P(Y = 0) =02.0

53130 1287

)!20(!5

!25

)!8(!5

!13

)!12(!0

!12 5 25 5 13 1 3 5 25 05 1225

12



                                                                            .

2.2 Both of these probabilities can be determined using the hypergeometric distribution:

• N = 20, n = 2, m = 15, k = 2

P(Y =2) =28.0

380 105

)!18(!2

!20

)!5(!0

!5

)!13(!2

!15 2 20

5 2 15 2 20 22 1520 2 15



                                                                           

• N = 20, n = 2, m = 15, k = 1

P(Y =1) =20.0

380 75

)!18(!2

!20

)!4(!1

!5

)!14(!1

!15 2 20 1 5 1 15 2 20 12 1520 1 15



                                                                           

• The expected number of students selected that are proficient in reading can be determined

by finding the mean of the hypergeometric distribution:

 = N

nm = 20

)15(2 = 1.5

Since we cannot select “half” students, we would expect both students selected to be proficient in reading. This makes intuitive sense, since the majority of the students are proficient in reading.

2.3 This probability can be determined using the hypergeometric distribution:

N = 100, n = 6, m = 48, k = 3

P(Y =3) =32.0

1192052400

382241600

)!94(!6

!100

)!49(!3

!52

)!45(!3

!48 6 100 3 52 3 48



                                                

2.4 This probability can be determined using the Bernoulli distribution. Two of the five applicants are female, so the proportion of female candidates is 2/5 = 0.4. Therefore, the probability of randomly selecting a female applicant is 0.4.

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