Deck 8: Measures of Association for Variables Measured at the Nominal Level

Question 1

A researcher has found a non-random relationship in a large random sample using hypothesis testing. Why would it be a good idea to also compute measures of association?

A) The researcher will want to assess the strength and direction of the relationship.
B) Hypothesis tests do not have sufficient power to detect important relationships in large samples.
C) Measures of association can sometimes contradict hypothesis test results, so both are needed for complete information.
D) Measures of association are not necessary if the null hypothesis has been rejected.

Answer 1

The researcher will want to assess the strength and direction of the relationship.

Question 2

Why are measures of association helpful in testing the validity of a theory?

A) Theories do not specify what the independent or dependent variable is in a relationship, so measures of association help clarify this point.
B) Theories seldom articulate cause-and-effect relationships, so measures of association help determine causality.
C) Theories stipulate that one variable causes another, so we need to know how strongly the independent variable is related to the dependent variable.
D) Measures of association are not helpful in testing a theory; they are used for research purposes where theory is not yet developed.

Answer 2

Theories stipulate that one variable causes another, so we need to know how strongly the independent variable is related to the dependent variable.

Question 3

Tests of significance reveal if results are non-random. What should a researcher use to investigate the strength and direction of relationships?

A) ANOVA
B) percentages
C) measures of association
D) chi square tests

Answer 3

measures of association

Question 4

Which element of research design influences tests of significance far more than it influences measures of association?

A) sample size
B) level of measurement
C) how the EPSEM sample was obtained
D) whether the association is positive or negative

Question 5

In what sense do measures of association help with prediction?

A) They show whether a relationship is causal.
B) They give us a better estimate of a case's score on the dependent variable than we would obtain by guessing.
C) They tell us whether an observed relationship is likely to have occurred by random chance.
D) They allow us to determine whether a theory is true or false.

Question 6

Which of these statements describes the variables if the distribution of the scores of one variable changes across the categories of another variable?

A) They are perfectly associated.
B) They are associated to some extent.
C) They have a cause-and-effect relationship.
D) They are related in a way that is statistically significant.

Question 7

If the independent (X) variable is located in the columns, and the dependent (Y) variable in the rows of a bivariate table, how would we inspect the table to understand a bivariate association?

A) Read down the rows to compare the conditional distributions of X.
B) Look across the columns to compare the conditional distributions of Y.
C) Look for the cell with the largest frequency value and compare it to the cell with the lowest frequency value.
D) Add the frequency values together and divide by the total frequency.

Question 8

Suppose chi square computed on a bivariate table is greater than zero. Which of these statements describes the variables?

A) They are not associated, and they are independent.
B) They are associated, and they may be dependent.
C) They are associated, and they are independent.
D) They are not associated, and they are not independent.

Question 9

How would a researcher reveal if variables are associated when the variables are arranged in a bivariate table?

A) by subtracting their scores horizontally
B) by computing percentages in the direction of the dependent variable
C) by computing percentages in the direction of the independent variable
D) by adding their scores vertically

Question 10

Which percentages should be computed in order to display the effects of the X variable on the Y variable in a bivariate table when the independent variable has been arranged in the columns?

A) those using n as the denominator
B) those within each column
C) those within each row
D) those between each column

Question 11

Suppose there is a perfect relationship between being convicted of a crime (X) and being sentenced to jail (Y) in a sample of criminal defendants. Which of the following statements can we conclude?

A) Just as many defendants not convicted of a crime were sentenced to jail as were those who were convicted.
B) All cases in each column of a bivariate table would be located in a single cell.
C) There is maximum variation in jail sentencing for each category of crime conviction.
D) We are unable to predict jail sentencing on the basis of crime conviction.

Question 12

Suppose the maximum difference calculated in a bivariate table is 23 percentage points. How should we describe the relationship?

A) as weak
B) as moderate
C) as strong
D) as causal

Question 13

Which one of the following patterns describes a positive association between two variables?

A) As one variable increases in value, the other also increases.
B) As one variable increases in value, the other stays the same.
C) As one variable decreases in value, the other increases.
D) Neither variable decreases.

Question 14

As age increases, memorization speed declines. What kind of relationship is this?

A) a negative relationship
B) a positive relationship
C) a non-linear relationship
D) a null relationship

Question 15

What is the association between variables if they vary in opposite directions?

A) neutral
B) contradictory
C) negative
D) positive

Question 16

A historical study of dietary patterns in the Middle Ages finds that, with increased wealth, people consumed more calories. How would this relationship be summarized statistically?

A) There was a negative association between wealth and caloric intake.
B) There was a positive association between wealth and caloric intake.
C) There was a perfect association between wealth and caloric intake.
D) There was either a moderate or a strong association between these variables, and there could not be a weak relationship.

Question 17

A researcher is interested in the association between gender (measured in two categories) and income (measured in three ordered categories: low, medium, high). What variable should dictate what measure of association is used?

A) gender
B) income
C) low income
D) Measures of association cannot be computed with these variables.

Question 18

What must be calculated before phi and Cramer's V can be computed?

A) lambda
B) maximum difference
C) clustered bar charts
D) chi square test

Question 19

Which of the following types of bivariate tables are appropriate for calculating phi?

A) 2 × 1
B) 2 × 2
C) 4 × 0
D) Bivariate tables of any size are appropriate for calculating phi.

Question 20

How is phi similar to Cramer's V?

A) Both first require calculating ÷².
B) Both are measures of proportional reduction in error (PRE).
C) Both provide a meaningful percentage of the explained variance in Y.
D) Both are useful for 4 × 4 bivariate tables.

Question 21

What is the major difference between Cramer's V and phi?

A) Cramer's V is suitable for tables larger than 2 × 2, and phi is not.
B) Phi is suitable for tables larger than 2 × 2, and Cramer's V is not.
C) Cramer's V gives us the direction of an association, and phi does not.
D) Phi gives us the direction of an association, and Cramer's V does not.

Question 22

For which of the following would phi and Cramer's V be appropriate as measures of association?

A) for variables measured at the nominal level
B) for variables measured at the interval-ratio level
C) for variables measured at the ordinal level
D) for variables measured at the continuous level

Question 23

In a 2 × 2 table, what is the range of phi?

A) 1 to 100
B) 0 to 1.00
C) 0 to 1.00.
D) -1.00 to +1.00

Question 24

Researchers are comparing Canadians and Americans on support (yes versus no) for subsidized child care. A phi of 0.21 was calculated for the relationship between nationality and support for the proposed childcare policy. What can we conclude?

A) Canadians are more supportive than Americans for subsidized child care.
B) There is a positive association between nationality and support for the policy.
C) There is a moderate association between the variables.
D) There is a strong association between the variables.

Question 25

Which of the following best describes how measures of proportional reduction in error (PRE) quantify association?

A) by comparing two predictions
B) by comparing two bivariate tables
C) by comparing expected and observed values in a bivariate table
D) by comparing two critical values

Question 26

What is the basis of our prediction for the first prediction in a proportional reduction in error (PRE) measure?

A) the most typical value of the dependent variable
B) the most typical value of the independent variable
C) the value of a dependent variable at a given value of the independent variable
D) the least common value from the dependent or independent variable-whichever is lower

Question 27

A researcher wants to predict fitness club membership, with income level as the independent variable. When ignoring income, the researcher's prediction results in 102 errors. When taking income into account, the number of errors falls to 56. What should be the conclusion?

A) Income causes differences in fitness club membership.
B) There is an association between income and fitness club membership.
C) There is no association between income and fitness club membership.
D) Phi will equal the value of lambda.

Question 28

How do we find E₂?

A) by subtracting the respective column totals from row totals, and dividing by n
B) by multiplying E₁ by n
C) by subtracting the column totals from the largest cell frequency in each column, and then adding subtotals together
D) by subtracting the largest cell frequency in each column from the column total, and then adding the subtotals

Question 29

Suppose we wish to understand the relationship between two variables: social class and film genre preference. Which of the following would be a reason to prefer lambda as a measure of association?

A) Lambda allows us to understand whether our sample was drawn randomly from a well-defined population.
B) Lambda gives us clear criteria for knowing whether the association is weak, moderate, or strong.
C) Lambda is a symmetrical measure of association, so we will get the same value even if we were to reverse the X and Y variables in our calculation.
D) Lambda allows us to quantify exactly how much knowing a person's social class helps to predict their film preference.

Question 30

In his thesis project, a student analyzes a 2 × 3 table with level of education (university degree versus less than university degree) predicting frequency of strenuous exercise (< weekly, weekly, > weekly). He finds that lambda = 0.48. What should his interpretation be?

A) Knowing how frequently a person exercises helps reduce our error in predicting education level by about half.
B) Knowing a person's education helps reduce our error in predicting exercise frequency by about half.
C) We can assume that there is a moderate relationship, but lambda lacks a PRE interpretation.
D) It is inappropriate to calculate lambda for a 2 × 3 table because it is not symmetrical. He should change the table to be 2 × 2 or 3 × 3 before computing lambda.

Question 31

A researcher assesses the relationship between countries' development (highly developed versus less highly developed) and whether or not the country has ever elected a female head of state. The lambda for this association is 0.28. The researcher is better off knowing about country development by what percentage?

A) 72%
B) 52%
C) 28%
D) 8%

Question 32

Lambda is considered an asymmetric measure of association. What does this mean?

A) Lambda can help reject a hypothesis, but it does not directly provide information about strength of association.
B) Lambda provides information about positive relationships, but not negative associations.
C) Lambda provides information about negative associations, but not positive relationships.
D) The value of lambda may vary depending on which variable is considered independent and which is considered dependent.

Question 33

Which one of the following can occur to lambda when the row marginals are extremely unequal?

A) Lambda may exceed 1.00.
B) Nothing, since lambda is not affected by row marginals.
C) Lambda may be less than zero.
D) Lambda may be zero even though there is an association between the variables.

Question 34

In a bivariate table, Cramer's V is 0.21 and lambda is 0. Which of the following should be our conclusion?

A) that the null hypothesis cannot be rejected; we have no evidence of an association
B) that the null hypothesis should be rejected, but we may have made a computation error when calculating lambda
C) that although V suggests a moderate relationship, lambda corrects our interpretation to indicate there is no relationship
D) that the variables may be associated even if lambda is zero, and disregard lambda if the row marginals are very unequal

Question 35

When should analysts be very cautious about using lambda as a measure of proportional reduction in error?

A) when both variables are measured at the nominal level
B) when the sample size is very large
C) when the bivariate table is larger than 2 × 2
D) when the row marginals are very unequal

Question 36

-Refer to the table. How should we calculate the conditional distribution of job satisfaction among those in unionized workforces?

A) (75/220) × 100 = 34%
B) (75/150) × 100 = 50%
C) ((75 + 220)/440) × 100 = 67%
D) ((75 + 220)/370) × 100 = 80%

Question 37

-Refer to the table. Which of these statements is the best way to describe the relationship between type of workplace and job satisfaction?

A) There is a weak positive association.
B) There is a moderate negative association.
C) There is an association, but it is impossible to determine its direction.
D) There is no association.

Question 38

-Refer to the table. Which of these statements would best describe the results if we drew a paralleled pie chart to depict the association between workplace type (unionized or non-unionized) and job satisfaction?

A) Two pies would be drawn, one for satisfied workers and one for unsatisfied workers; the pie for unsatisfied workers would be larger.
B) Two pies would be drawn, one for satisfied workers and one for unsatisfied workers; both would have identical pie slice sizes.
C) Two pies would be drawn, one for unionized workers and one for non-unionized workers; they would have identical pie slice sizes.
D) Four pies would be drawn, the biggest slices of which would correspond to non-unionized workers.

Question 39

-Refer to the table. What is E₁?

A) 10
B) 50
C) 55
D) 70

Question 40

-Refer to the table. What is E₂?

A) 30
B) 45
C) 55
D) 70

Question 41

-Refer to the table. What is lambda?

A) 0.82
B) 0.45
C) 0.33
D) 0.25

Question 42

Measures of association enable prediction. Explain whether prediction requires a causal relationship between the variables.

Question 43

Describe the difference between the "dependent-only prediction rule" and the "relational prediction rule" when applying a proportional reduction in error (PRE) approach.