Chapter 9: Numbers, Comparisons, and Calculations

Test Bank

Multiple Choice

1. What does the term “level” refer to, in the context of numbers?

A. level of measurement

B. numeric value of a measure

C. level of aggregation of a unit

D. system of measurement

Learning Objective: 9-1: Identify frequently-used measures of level or value.

Cognitive Domain: Knowledge

Answer Location: Value or Level

Difficulty Level: Easy

2. What is a “real” number?

A. a number with a positive value

B. a number with no decimals

C. a discrete valued number

D. a number with or without decimals

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Knowledge

Answer Location: Value or Level

Difficulty Level: Easy

3. How is “prevalence” different from “incidence?”

A. It gives all cases at a time point, not just new cases.

B. It shows only new cases at a time point, not all cases.

C. It quantifies the flow and not the stock of a variable.

D. It gives the mean value, and not the total value.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Comprehension

Answer Location: Incidence and Prevalence

Difficulty Level: Easy

4. An online feedback form, maintained by a courier service company, asks customers with complaints to mark a number from 1 to 10 after interacting with customer care, with 1 denoting very dissatisfied, and 10 denoting extremely satisfied. What is this feedback called?

A. customer points

B. Likert-type scale

C. rating

D. assessment

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Rating

Difficulty Level: Medium

5. How is the term “risk” defined in the context of quantitative research?

A. high incidence of a particular event

B. probability of occurrence of an event

C. prevalence of an event over a period

D. ratio of flow over stock of a variable

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Knowledge

Answer Location: Risk

Difficulty Level: Easy

6. Among 2,000 widgets produced by a manufacturing company in 2 hr, seven widgets are found to be defective, on average. What is the defective rate of widgets per 2,000 units produced?

A. .00175

B. .175%

C. .007

D. .35%

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Rates

Difficulty Level: Medium

7. What kind of measure is associated with a retail savings account bank balance?

A. count

B. integer

C. real

D. rating

Learning Objective: 9-2: Assess plausibility of values for measures of level.

Cognitive Domain: Application

Answer Location: Plausibility Criteria for Measures of Level

Difficulty Level: Medium

8. The topic or context has minimal effect on plausible values for which of the following measures?

A. real

B. count

C. integer

D. rating

Learning Objective: 9-2: Assess plausibility of values for measures of level.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Measures of Level

Difficulty Level: Easy

9. Which of the following measures is used for auto insurance claims made in the year 2020 by policyholders of an insurance company?

A. integer

B. count

C. rating

D. real

Learning Objective: 9-2: Assess plausibility of values for measures of level.

Cognitive Domain: Application

Answer Location: Plausibility Criteria for Measures of Level

Difficulty Level: Medium

10. What are the upper and lower limits of a percentile distribution of values?

A. 0 and 99

B. 1 and 10

C. 1 and 100

D. 0 and 9

Learning Objective: 9-3: Apply common measures of position in a list (rank).

Cognitive Domain: Knowledge

Answer Location: Percentile

Difficulty Level: Easy

11. A student's SAT score was placed in the 75th percentile. What does this indicate?

A. The raw score received by the student was 75 points.

B. The student scored higher than 74% of examinees..

C. The sat score obtained by the student was 75%.

D. The student scored higher than 75% of examinees.

Learning Objective: 9-3: Apply common measures of position in a list (rank).

Cognitive Domain: Application

Answer Location: Percentile

Difficulty Level: Medium

12. What kind of a distribution is given by a quintile?

A. intervals of 10 percentiles

B. ranges of 25 percentiles

C. ranges of 20 percentiles

D. class of five percentiles

Learning Objective: 9-3: Apply common measures of position in a list (rank).

Cognitive Domain: Knowledge

Answer Location: Percentile

Difficulty Level: Easy

13. In which case could the highest rank number be less than the total number of values in a sorted list?

A. If some values in the list are tied

B. When there are ordinal values in the list

C. If some of the values are equal to zero

D. When one or more values are missing

Learning Objective: 9-4: Evaluate plausibility of values for measures of rank.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Measures of Position

Difficulty Level: Medium

14. Why are limits on rank in a sorted list not affected by the topic or context of study?

A. Rank is converted to one unit.

B. Rank is an absolute number.

C. Position is equidistant for any topic.

D. All positions have the same limits.

Learning Objective: 9-4: Evaluate plausibility of values for measures of rank.

Cognitive Domain: Comprehension

Answer Location: Plausibility Criteria for Measures of Position

Difficulty Level: Medium

15. Under what situation is an absolute difference between two values at two time points not a good measure?

A. The second value is significantly smaller than the first.

B. The values are represented as logarithmic values.

C. The magnitude of the values is vastly different by context.

D. The topic is in the domain of the medical sciences.

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Knowledge

Answer Location: Subtraction

Difficulty Level: Medium

16. What does a ratio greater than 1 indicate?

A. Value of interest is smaller than the reference value.

B. The comparison group is smaller than the value of interest.

C. The comparison value is greater than the mean value.

D. Value of interest is greater than the reference value.

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Knowledge

Answer Location: Division

Difficulty Level: Easy

17. Why is a ratio usually a better calculation than a simple difference?

A. It adjusts for magnitude of the base value by context.

B. It provides a smaller number for comparison.

C. It can be represented by any measure.

D. It can be converted into a percentage value.

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Comprehension

Answer Location: Division

Difficulty Level: Medium

18. The annual gross revenue of a local pharmacy store in Key West, FL, dropped from $2,132,000 in 2018 to $1,608,050 in 2019. What is the comparison ratio of revenue with respect to 2019?

A. 1.326

B. 0.754

C. –1.326

D. –0.754

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Application

Answer Location: Division

Difficulty Level: Medium

19. How is “relative risk” calculated?

A. outcome value of exposed group by outcome value of unexposed group

B. outcome value of unexposed case by dependent value of exposed case

C. outcome values of exposed group at two time periods divided in order

D. outcome value of exposed group multiplied by a risk factor

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Knowledge

Answer Location: Relative Risk

Difficulty Level: Easy

20. How could a proportion be converted to a percentage?

A. divide by 100

B. multiply by 100

C. multiply by base value

D. divide by base value

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Knowledge

Answer Location: Percentage or Proportion of a Whole

Difficulty Level: Easy

21. A “percentage of” expresses the numerator as a percent of which value?

A. risk factor

B. numerator of first time point

C. difference of two values

D. denominator

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Knowledge

Answer Location: Relationship Between Ratio and Percentage of

Difficulty Level: Easy

22. Darryl scored 85 in a math test, whereas Peter scored 32 on the same test. What is the percent difference in score for Peter?

A. 62.35%

B. 166.62%

C. 37.65%

D. 265.63%

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Application

Answer Location: Percentage Difference

Difficulty Level: Hard

23. What is the difference between a percent change and a percent difference?

A. Percent change is for different locations, percent difference is for the same location.

B. Percent change is for the same topic, percent difference is for two topics

C. Percent change is for two time points, percent difference is for the same time point.

D. Percent change is used in social sciences, percent difference is used in statistics.

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Knowledge

Answer Location: Percentage Change

Difficulty Level: Easy

24. Why is a ratio not affected by the system of measurement?

A. They are always converted to the same unit.

B. The units cancel out in the calculation.

C. They are used only for identical units.

D. They are used only for the same context.

Learning Objective: 9-6: Assess plausibility of values for different types of numeric comparisons.

Cognitive Domain: Comprehension

Answer Location: Plausibility Criteria for Results of Calculations

Difficulty Level: Easy

25. What can be determined when comparing two values of a nominal variable?

A. One is greater than the other.

B. One is ranked lower than the other.

C. They are the same or they are different.

D. They are equal in value.

Learning Objective: 9-7: Understand how a variable’s level of measurement determines which types of comparisons and calculations can be conducted with values of that variable.

Cognitive Domain: Comprehension

Answer Location: Qualitative Variables

Difficulty Level: Medium

True/False

1. The level of measurement of a variable determines the type of comparison and mathematical calculation that are possible for values of the variable.

Learning Objective: 9-7: Understand how a variable’s level of measurement determines which types of comparisons and calculations can be conducted with values of that variable.

Cognitive Domain: Knowledge

Answer Location: Quantitative Variables

Difficulty Level: Easy

2. The direction of association between two values can be determined for an interval variable but not for an ordinal variable.

Learning Objective: 9-7: Understand how a variable’s level of measurement determines which types of comparisons and calculations can be conducted with values of that variable.

Cognitive Domain: Knowledge

Answer Location: Quantitative Variables

Difficulty Level: Medium

3. When reporting a percentage change, the base value should also be stated.

Learning Objective: 9-8: Choose comparisons and calculations to suit the research topic and field.

Cognitive Domain: Knowledge

Answer Location: Choosing Types of Comparisons

Difficulty Level: Easy

4. Magnitude of risks that differ by context are usually reported as relative risks.

Learning Objective: 9-8: Choose comparisons and calculations to suit the research topic and field.

Cognitive Domain: Knowledge

Answer Location: Influence of Topic and Field

Difficulty Level: Easy

5. Level of measurement of a variable could also be termed as the “level” of the variable.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Comprehension

Answer Location: Numeric Measures of Level

Difficulty Level: Medium

6. The frequency or count of a categorical variable by its categories are whole numbers.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Comprehension

Answer Location: Value or Level

Difficulty Level: Medium

7. Values of dimensions of rooms in an apartment are always denoted as whole numbers.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Value or Level

Difficulty Level: Easy

8. Variables measured as real numbers have minimal effect on their plausible values.

Learning Objective: 9-2: Assess plausibility of values for measures of level.

Cognitive Domain: Comprehension

Answer Location: Plausibility Criteria for Measures of Level

Difficulty Level: Medium

9. The units of “rank” are the position numbers in an ordered list, and not the units of the variable values in the list.

Learning Objective: 9-3: Apply common measures of position in a list (rank).

Cognitive Domain: Knowledge

Answer Location: Rank

Difficulty Level: Easy

10. The lowest value of a percentile distribution is first percentile.

Learning Objective: 9-4: Evaluate plausibility of values for measures of rank.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Measures of Position

Difficulty Level: Medium

Short Answer

1. The precision level of dimensions of a widget has been set to .0001 cm (centimeters) by the quality department of a manufacturing company. What type of measure is used for these dimensions? Explain your answer.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Value or Level

Difficulty Level: Easy

2. Provide an example that distinguishes “incidence” from “prevalence.” Explain the two terms with the help of your example.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Incidence and Prevalence

Difficulty Level: Medium

3. Explain the importance of interpreting the scale of a rating correctly. With the help of an example, show the consequences of misinterpreting the scale.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Comprehension

Answer Location: Rating

Difficulty Level: Hard

4. Give an example where the concept and units are different for the numerator and denominator of a ratio.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Ratios

Difficulty Level: Hard

5. In your own words, define the term “risk” in the context of research. Illustrate with an example.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Comprehension

Answer Location: Risk

Difficulty Level: Medium

6. Discuss the limits on values of an integer measure, and, whether the topic or context have an effect on plausible values of the measure. Illustrate with an example.

Learning Objective: 9-2: Assess plausibility of values for measures of level.

Cognitive Domain: Comprehension

Answer Location: Plausibility Criteria for Measures of Level

Difficulty Level: Medium

7. Explain the difference between position in an ordered list and the measure of values in the list. Give an example to show this difference.

Learning Objective: 9-3: Apply common measures of position in a list (rank).

Cognitive Domain: Comprehension

Answer Location: Rank

Difficulty Level: Medium

8. With the help of an example, explain the difference between a decile and a quartile distribution of values.

Learning Objective: 9-3: Apply common measures of position in a list (rank).

Cognitive Domain: Application

Answer Location: Percentile

Difficulty Level: Medium

9. What are the definitional limits of a decile and a quintile distribution of values? Illustrate with an example.

Learning Objective: 9-4: Evaluate plausibility of values for measures of rank.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Measures of Position

Difficulty Level: Medium

10. The risk of being affected by a particular virus was 1 in a 1,000 for people who had not been vaccinated against the virus. For those who had been vaccinated against the virus, the risk was 1 in 15,000. What is the relative risk of catching the virus?

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Application

Answer Location: Relative Risk

Difficulty Level: Medium

Essay

1. Design a research study on a particular topic of your choice. You may use any studies you had designed in the previous chapters. In addition to the outcome variable, you should have at least three independent variables in the study. Discuss the measures and their definitional limits for each of the variables used in your study.

Learning Objective: 9-1: Identify frequently used measures of level or value.

Cognitive Domain: Application

Answer Location: Numeric Measures of Level

Difficulty Level: Medium

2. During exploratory analysis of the variables in the study you designed in Question 1, what types of calculations would you conduct in order to compare values? Explain your choices of calculations.

Learning Objective: 9-5: Use different types of mathematical calculations to compare numbers.

Cognitive Domain: Application

Answer Location: Mathematical Calculations

Difficulty Level: Hard

3. Discuss the plausibility of values for the calculations you chose in Question 2. What effect does the topic or context have on the plausible values?

Learning Objective: 9-6: Assess plausibility of values for different types of numeric comparisons.

Cognitive Domain: Application

Answer Location: Plausibility Criteria for Results of Calculations

Difficulty Level: Hard