Deck 9: Measures of Association for Variables Measured at the Ordinal Level

Question 1

Which of the following is an appropriate measure of association for ordinal level variables with only a few categories or values?

A) chi square
B) Cramer's V
C) Spearman's rho
D) gamma

Answer 1

gamma

Question 2

Which of the following is a major difference between a "continuous ordinal variable" and a "collapsed ordinal variable"?

A) Only continuous ordinal variables can be used in a bivariate table.
B) Only collapsed ordinal variables can have measures of association calculated.
C) Collapsed ordinal variables have fewer categories and can apply a greater number of measures of association than continuous ordinal variables.
D) Continuous ordinal variables use pairs of respondents in the calculation of association, whereas collapsed ordinal variables use chi square based statistics.

Answer 2

Collapsed ordinal variables have fewer categories and can apply a greater number of measures of association than continuous ordinal variables.

Question 3

A bivariate table has 115 pairs of cases ranked the same and 74 pairs of cases ranked dissimilarly. What could we conclude about the relationship in this table?

A) The relationship is negative.
B) The relationship is positive.
C) It is impossible to calculate gamma or Somers' d, so the nature of the relationship cannot be known.
D) The relationship is neutral.

Answer 3

The relationship is positive.

Question 4

What does a value of "0" indicate for gamma?

A) There are more dissimilar pairs than similar pairs.
B) There are more similar pairs than dissimilar pairs.
C) There is an equal number of similar and dissimilar pairs.
D) There are no similar pairs.

Question 5

What is indicated by the fact that a researcher found a gamma of +0.37 for a relationship involving education and public library use?

A) that people with limited funds have greater need for free public libraries
B) that library use increases with education
C) that the well-educated are more likely to purchase books
D) that as education increases, people are less likely to go to the library

Question 6

In the formula for gamma, what does n_s represent?

A) the number of pairs of cases that have the same score
B) the number of pairs of cases in all similar cells
C) the number of pairs of cases ranked the same on both variables
D) the number of pairs of cases in all cells

Question 7

In the formula for gamma, what does n_d represent?

A) the number of pairs of cases with low scores
B) the number of pairs of cases in all dissimilar cells
C) the number of pairs of cases that have different scores on either variable
D) the number of pairs of cases ranked differently on both variables

Question 8

Which of the following statistics has a PRE (proportional reduction in error) interpretation?

A) gamma
B) Kendall's tau-b
C) Somers' d
D) Kendall's tau-c

Question 9

Which of the following is a limitation of gamma?

A) It ignores pairs that are tied and can inflate the estimate of association.
B) It fails to tell us whether values of X help predict values of Y.
C) It is not on a clearly interpretable 0 to ±1 scale like other measures of association.
D) It has a more complicated formula than Kendall's tau-b and Somers' d.

Question 10

What is indicated by the fact that a researcher found a Kendall's tau-b of -0.45 for the relationship between social class and religious service attendance?

A) that no relationship exists between these variables
B) that people from upper classes are less likely to attend religious services
C) that upper class people are more likely to attend religious services
D) that as social class increases so does religious service attendance

Question 11

Which of these statements describes a symmetric measure of association?

A) Its values are just as likely to be negative as positive.
B) Its values will be the same regardless of which variable is assumed to be independent.
C) Its values cannot exceed the value of the highest score.
D) Its values cluster around the centre of the range of scores.

Question 12

What is the range of Somers' d?

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

Question 13

A researcher has computed a Somers' d of -0.75 between marital happiness and number of children. What can be concluded from this result?

A) that families with more children are happier
B) that children have a strong, positive influence on levels of marital happiness
C) that number of children and marital happiness are causally related
D) that there is a strong, negative relationship between number of children and marital happiness

Question 14

In a large sample of Canadians, adults in higher social classes (e.g., upper-middle class) are more likely to report exercising on a daily basis than on a monthly basis. Adults in lower social classes (e.g., working class) are more likely to report exercising on a monthly basis than on a daily basis. What best characterizes this association?

A) no association
B) positive association
C) negative association
D) a curvilinear association

Question 15

A sociologist wishes to assess the association between two ordinal variables, both consisting of 12 categories. The researcher decides to collapse the categories into a dichotomous form (categories 1-5 = "high" versus categories 6-12 = "low") and then produce a bivariate table. Is this a good idea?

A) No. The researcher is left without statistical measures of association: Cramer's V or phi can no longer be used to assess bivariate association.
B) No. Information is thrown away: The researcher must assume that different scores within the "high" or "low" categories are not meaningful.
C) Yes. Measures for ordinal association cannot be used for variables with more than 10 variables.
D) Yes. If the researcher wishes to impose an arbitrary division point on a variable with many categories, it will greatly simplify the analysis.

Question 16

A teacher asks his students to rate the difficulty of tests in his class from 1 to 10, and overall satisfaction with the class from 1 to 10. He thinks that students finding the tests less difficult will tend to be more satisfied with their experience in the class. What would be the ideal measure of association to test this idea?

A) Spearman's rho
B) Somers' d
C) phi
D) lambda

Question 17

What is the first step for calculating Spearman's rho?

A) calculating the range for each variable
B) calculating the range for each variable and dividing by 2
C) calculating the average value for each variable
D) ranking the scores from each variable from high to low

Question 18

Which of these values of Spearman's rho indicates the strongest relationship between two ordinal variables?

A) rho = 0.60
B) rho = 0.00
C) rho = -0.80
D) It is impossible to say.

Question 19

Why are chi square tests not ideal for testing the statistical significance of measures of association between ordinal variables?

A) Degrees of freedom for chi square tests are dependent on sample size, whereas degrees of freedom for tests of no association with gamma are not dependent on sample size.
B) Chi square tests cannot be calculated on an EPSEM sample.
C) Chi square tests can only be calculated for bivariate tables with the same number of rows and columns.
D) Chi square tests only whether the cell frequencies occurred by chance, not whether the association is different from the null value of 0.

Question 20

Which of the following is a violation of the assumptions of a test of statistical significance for gamma?

A) The bivariate table is 3 × 3.
B) Both variables were measured on the ordinal scale, not as nominal variables.
C) The sample size is too large to have confidence in the calculation.
D) The sample was drawn by convenience, not by EPSEM procedures.

Question 21

A researcher states a null hypothesis that the relationship between marital satisfaction and happiness is characterized by Spearman's rho = 0. What does the researcher need to assume about the sampling distribution of rho?

A) It has a chi square sampling distribution.
B) It has a non-random sampling distribution.
C) It has a normal sampling distribution.
D) It has no sampling distribution.

Question 22

Which of the following could be concluded if a researcher rejects the null hypothesis in a test of significance for a Spearman's rho?

A) that the variables are likely related in the population
B) that the relationship between the variables is negative
C) that no inference can be made about the relationship of the two variables in the population
D) that the relationship exists but its direction and strength are unknown

Question 23

A researcher interviews the mayors of nine Canadian cities. She wants to determine whether size of the city (small, medium, or large) is associated with its mayor's assessment of clinic availability (unsuitable, acceptable, excellent).

-Refer to the scenario. How many unique pairs are there for calculating the measure of association?

A) 3
B) 9
C) 36
D) 81

Question 24

A researcher interviews the mayors of nine Canadian cities. She wants to determine whether size of the city (small, medium, or large) is associated with its mayor's assessment of clinic availability (unsuitable, acceptable, excellent).

-Refer to the scenario. Which of the following would be an ideal measure of association to calculate if the researcher re-did the study with 100 cities, and decided to measure size of city with five categories (very large, large, medium, small, very small) rather than three?

A) Kendall's tau-b
B) Kendall's tau-c
C) Cramer's V
D) phi

Question 25

The table shows a relationship between length of residency in a low-income neighbourhood and support for a city's redevelopment plans for the neighbourhood.


-Refer to the table. How should the relationship between residency and support be described?

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

Question 26

-Refer to the table. If we were to compute Spearman's rho, who would receive rank 1 for Y?

A) Maxine
B) Jorge
C) Phillip
D) Tory

Question 27

-Refer to the table. What should the sum of the D column be?

A) +0
B) 28
C) 33
D) There is not enough information in the table to compute ?D².

Question 28

There are many statistics for the association between two ordinal variables. Briefly explain what considerations determine which one is appropriate.

Question 29

Is there an association between life satisfaction and sexual frequency? Calculate percentages and Kendall's tau-b for the table below and write a sentence or two assessing the strength and direction of the relationship.

Question 30

Scales have been administered to 11 employees of a large corporation to measure their job satisfaction (25-point scale) and the prestige (100-point scale) of their occupations. Higher scores indicate greater satisfaction and more prestige. Calculate Spearman's rho and write a sentence or two analyzing the strength and direction of the relationship.