Deck 11: Bivariate Association for Nominal- and Ordinal-Level Variables

Question 1

The distribution of scores on the dependent variable for a specific category of the independent variable is called

A) associated categories
B) the distribution correlation
C) the conditional distribution of Y
D) the marginal response category

Answer 1

the conditional distribution of Y

Question 2

If the distribution of the scores of one variable changes across the categories of another variable, the variables

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

Answer 2

are associated to some extent

Question 3

If social class is a cause of a person's political ideology, then ___________ is the independent variable and ___________ is dependent.

A) class … ideology
B) ideology … class
C) person … ideology
D) information is not sufficient to tell which is independent and which dependent

Answer 3

class … ideology

Question 4

In a bivariate table, the categories of the dependent variable are placed in the

A) rows
B) columns
C) marginals
D) far right-hand column

Question 5

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, compute percentages

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

Question 6

A researcher has found a strong relationship between level of education and income and concludes that "higher levels of education cause higher income." What error has been made?

A) None, the argument is sound
B) Income is only nominal in level of measurement and education is ordinal so they cannot be causally related
C) Since these variables are continuous and interval ratio, they cannot have a causal relationship
D) By itself, association does not prove causation

Question 7

Tests of significance and measures of association provide information about sample data that is

A) complimentary
B) contradictory
C) unnecessary
D) redundant

Question 8

Conventionally, each column of a bivariate table represents

A) the highest scores of each variable
B) a category of the independent variable (X)
C) a category of the dependent variable (Y)
D) the lowest scores on each variable

Question 9

For variables measured at the ordinal and interval-ratio levels, measures of association will have a lower limit of _______ and an upper limit of ________

A) 0 … 100
B) 0 … ±1
C) 0 … 1
D) 1 … 0

Question 10

Tests of significance tell us if our results are non-random. To investigate the strength and direction of relationships, we must use

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

Question 11

In the case of a perfect association, predictions from one variable to another can be made

A) only if variables are measured at the nominal level
B) when at least one variable is ordinal
C) without error
D) only if the relationship is positive

Question 12

For variables measured at the nominal level, measures of association will have a lower limit of _______ and an upper limit of _______

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

Question 13

If variables are arranged in a bivariate table, we can see if they are associated by

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

Question 14

Measures of association

A) increase our understanding of causal relationships among variables
B) provide proof of causal relationships among variables
C) enhance our ability to predict from one variable to another
D) both a and c

Question 15

Measures of association help social scientists accomplish two important goals

A) prediction and forecasting
B) understanding causation and measuring concepts
C) prediction and correlation
D) prediction and understanding causation

Question 16

A researcher can demonstrate a strong association between gender and income. Which variable is independent?

A) gender
B) both
C) income
D) neither

Question 17

With the independent variable in the columns, the "maximum difference" is the largest difference

A) in column percents in any row
B) in row percents in any column
C) between the marginals
D) between any two cell frequencies

Question 18

If there is an association between two variables,

A) the scores of the cases are approximately equal
B) the distributions of the scores approach normality
C) all of the scores are in the same row in the bivariate table
D) the conditional distributions of Y change

Question 19

If the maximum difference is greater than 30, the relationship is

A) strong
B) moderate
C) weak
D) statistically significant

Question 20

If the conditional distributions of Y do not change across the categories of X, any measure of association and the maximum difference would be

A) 1.00
B) 0.00
C) 0.10
D) 100

Question 21

"As education increases, income rises." This is an example of a

A) non-causal relationship
B) positive relationship
C) negative relationship
D) neutral relationship

Question 22

When variables vary in opposite directions, the association between variables is said to be

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

Question 23

For a 3 x 3 table, the appropriate chi square based measure of association would be

A) Cramer's V
B) phi
C) lambda
D) gamma

Question 24

If there is a positive association between two variables,

A) as one variable increases in value, the other also increases
B) as one variable decreases in value, the other increases
C) the researcher can be certain of his conclusions
D) neither variable can decrease

Question 25

"As the temperature rises, the crime rate increases."

A) This is a positive relationship.
B) If the temperature falls below zero degrees, there is no crime
C) If the temperature would remain stable, the crime rate would stay the same
D) Criminals should be incarcerated in Alaska

Question 26

Lambda is a PRE measure that is used when variables are measured at the

A) nominal level
B) ordinal level
C) interval-ratio level
D) any of the above

Question 27

A researcher finds that income decreases as length of commute increases. This is a ________ relationship

A) positive
B) important
C) negative
D) associational

Question 28

A problem with both Cramer's V and phi is that values between 0.00 and 1.00

A) are very rare
B) are mathematically impossible
C) can actually indicate negative relationships
D) can be interpreted only as an index of the relative strength of the association

Question 29

A study was made of marital satisfaction experienced by men and women. A phi of .07 was calculated for the relationship between gender and satisfaction. This result shows that

A) women experience greater marital satisfaction
B) men experience greater marital satisfaction
C) there is a weak relationship between the variables
D) there is a positive relationship between the variables

Question 30

Proportional reduction in error (PRE) measures of association are based on the logic of

A) percentages
B) inference
C) prediction
D) zero errors

Question 31

A researcher tested the relationship between gender and support for assisted suicide ("death with dignity") and found a Cramer's V of 0.45. This relationship is

A) strong
B) weak
C) positive
D) significant but not important

Question 32

According to the logic of proportional reduction of error (PRE), if two variables are associated then information about the independent variable

A) eliminates errors in the prediction of the dependent variable
B) reduces the number of errors in predicting the dependent variable
C) has no effect on the ability to predict the dependent variable
D) decreases errors of prediction for negative relationships and increases errors for positive relationships

Question 33

In tables larger than 2x2, the upper limit of phi

A) can be greater than 1.00
B) can be less than zero
C) is no more than 0.05
D) is 100

Question 34

If there is a perfect association between sexual attraction and accelerated heartbeat, then

A) sex is unhealthy
B) there is strong evidence that sexual attraction and accelerated heartbeat are causally related
C) if there is no sexual attraction, the heartbeat never accelerates
D) whenever the heartbeat accelerates, people become sexually attractive

Question 35

If you would like to compute a chi-square based measure of association for a 3x4 table, the appropriate measure would be

A) Cramer's V
B) phi
C) lambda
D) the maximum difference

Question 36

A researcher tested the relationship between education and support for assisted suicide ("death with dignity") and found that support increased as education increased and that the maximum difference was 45. This relationship is

A) strong negative
B) weak positive
C) strong positive
D) significant but not important

Question 37

In the formula for Cramer's V, the expression (minimum of r-1, c-1)

A) appears in the numerator
B) tells us to use phi if there are fewer than 3 rows or columns
C) is in the denominator
D) is used only for samples larger than 100

Question 38

Phi and Cramer's V would be appropriate as measures of association for variable measured at the

A) nominal level
B) ordinal level
C) interval-ratio level
D) any level of measurement

Question 39

A researcher finds that males are much more supportive of cohabitation than females. The phi is 0.25.This is a __________ relationship.

A) moderate
B) negative
C) positive
D) strong

Question 40

Lambda compares the number of errors of prediction under two separate rules. In the first rule, the independent variable is

A) ignored
B) squared
C) taken into account
D) expressed as a percentage

Question 41

For the same bivariate table, Cramer's V is .27 and lambda is zero. What can we conclude?

A) a computational mistake has been made. V can never be greater than lambda
B) this is a negative relationship
C) there is no association, disregard V
D) the variables may be associated even if lambda is zero. Disregard lambda if the row marginals are very unequal

Question 42

A researcher is interested in the relationship between social class (measured as upper, middle, or lower) and support (measured as strong, moderate, or weak) for a program of welfare reform. An appropriate measure of association for these two variables would be

A) Spearman's rho
B) Phi
C) Pearson's r
D) Gamma

Question 43

Gamma measures the proportional reduction in error when predicting

A) the order of pairs of cases on one variable
B) the order of pairs of cases on both variables
C) the order of a pair of cases on one variable with knowledge of the order of the pair on the other variable
D) none of the above

Question 44

In the case of gamma, a negative relationship means that

A) if case A ranks below case B on one variable, case A will rank below case B on the other variable
B) if case A ranks above case B on one variable, it will rank below case B on the other variable
C) if case A ranks above case B on one variable, it will rank above case B on the other variable
D) the ranking of cases will be unrelated

Question 45

Gamma and lambda are based on the logic of

A) chi square
B) associational percentages
C) proportional repartitioning
D) proportional reduction in error

Question 46

For ordinal level variables with only a few categories or values, an appropriate measure of association would be

A) Spearman's rho
B) Gamma
C) Chi square
D) Cramer's V

Question 47

If we cannot reduce our errors of prediction for the order of pairs of cases on one variable by predicting from the order of pairs of cases on the other variable

A) gamma will be zero
B) the association is moderate in strength
C) the relationship is positive
D) the relationship is negative

Question 48

Gamma is based on two prediction rules. In the first, we ______ and in the second we _________.

A) ignore X, take X into account
B) ignore Y, take X into account
C) ignore X, take Y into account
D) ignore both X and Y, take only Y into account

Question 49

A bivariate table shows the association between gender and whether or not a person ever attends formal religious services. Lambda was .34. What may be concluded?

A) women are more likely to attend church
B) men are more likely to attend church
C) knowing a person's gender improves our ability to predict whether or not they attend religious services by 34%
D) knowing whether a person attends religious services improves our ability to predict their gender by 34%

Question 50

Since gamma is a PRE measure, it tells us

A) the improvement in predicting the order of pairs of cases by taking the dependent variable (Y) into account
B) the improvement in predicting the order of pairs of cases by taking the independent variable (X) into account
C) how much better off we are by knowing the value of the independent variable
D) how much is gained by having full knowledge of both scores for each case

Question 51

For the relationship between social class and movie attendance, a researcher found a gamma of - 0.45. This indicates that

A) as social class increases, so does movie attendance
B) rich people watch more movies than poor people
C) there is no relationship between these variables
D) people from higher social classes are less likely to attend movies

Question 52

Information derived from survey data that examines the relationship between the race of a person and his employment status yields a lambda of .20. This information indicates that we are ______ % better off knowing race when attempting to predict employment status.

A) 50
B) 40
C) 80
D) 20

Question 53

If there is no association between two variables, knowledge of the independent variable

A) causes us to make more prediction errors
B) improves the accuracy of our predictions
C) does not change the number of errors of prediction
D) makes prediction of the dependent variable impossible

Question 54

While ignoring the independent variable, we make 78 errors when predicting the dependent variable. When taking the independent into account, we reduce the number of errors to 43. Therefore

A) the variables are not associated
B) the variables are associated
C) the independent variable is definitely a cause of the dependent variable
D) phi will be 0

Question 55

For a relationship involving education and library use, gamma was +0.37. This indicates that

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

Question 56

For the relationship between social class and movie attendance, a researcher found a gamma of - 0.45. This relationship is

A) weak and negative
B) strong and positive
C) negative and moderate
D) moderate and weak

Question 57

When the row marginals are extremely unequal,

A) lambda is the preferred measure of association
B) lambda may exceed 1.00
C) any chi square based measure of association will be less than zero
D) lambda may be zero even though there is an association between the variables

Question 58

Gamma ranges from

A) 0.00 to 1.00
B) 1.00 to 100
C) 0.00 to -1.00
D) -1.00 to +1.00

Question 59

Which is the correct expression for finding E1?

A) N - k
B) N - E2
C) phi - V
D) N - (largest row total)

Question 60

In the case of gamma, a positive relationship means that

A) if case A ranks below case B on one variable, case A will rank below case B on the other variable
B) if case A ranks above case B on one variable, it will rank below case B on the other variable
C) if case A ranks below case B on one variable, it will rank above case B on the other variable
D) the ranking of cases will be unrelated

Question 61

Ordinal level scales measuring religiosity and personal happiness range from 0 to 100. Which measure of association would be most appropriate to assess the relationship between these two variables?

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

Question 62

The square of Spearman's rho is the proportional reduction in error when predicting

A) rank on one variable from rank on the other variable compared to predicting rank while ignoring the other variable
B) the rank of a case from its score
C) rank on gamma vs. rank on phi
D) score on X while ignoring Y

Question 63

Gamma provides a summary measure of the

A) existence of a bivariate relationship
B) strength of a relationship
C) direction of a relationship
D) all of the above

Question 64

In computing Spearman's rho, the sum of the D column must be

A) 1
B) N
C) 0
D) the mean rank squared

Question 65

For a relationship involving education and library use, gamma was +0.37. This relationship is

A) weak and positive
B) strong and negative
C) moderate and positive
D) positive and weak

Question 66

A researcher has computed a gamma of -0.45 between marital happiness and number of children. What can she conclude?

A) families with more children are happier. This is a moderate relationship
B) children have a strong, positive influence on levels of marital happiness
C) there is a moderate, negative relationship between number of children and marital happiness
D) there is a weak, negative relationship between the variables

Question 67

Spearman's rho is appropriate for ordinal level variables because it is computed from

A) raw scores
B) the square root of gamma
C) ranks, not scores
D) percentiles, not ranks

Question 68

Spearman's rho is appropriate for use with

A) continuous ordinal variables
B) b variables whose categories have been collapsed
C) tables larger than 2x2
D) negative relationships only

Question 69

A study of the effects of fluoride in the water supply on level of calcium deficiency in women found a Spearman's rho of +0.30. Our PRE for this relationship is

A) 30%
B) 90%
C) 3%
D) 9%

Question 70

A gamma computed on the relationship between marital happiness and amount of TV viewing is +0.78. This means that

A) if we know how pairs of couples compare on TV viewing, we would be 78% better off predicting their ranks on marital happiness
B) happily married couples don't watch TV
C) couples that watch a lot of TV tend to be unhappy
D) TV causes divorce

Question 71

In the formula for gamma, Ns represents the number of pairs of cases

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

Question 72

In the formula for gamma, Nd represents the number of pairs of cases

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

Question 73

To compute Spearman's rho, we

A) rank the scores from each variable from high to low
B) take the difference between each score and the mean
C) estimate the mean rank squared
D) ignore all tied scores

Question 74

Like lambda and gamma, Spearmans' rho can be interpreted by the logic of

A) proportional reduction in error
B) hypothesis sorting
C) critical ranking analysis
D) semi-proportionate elliptical probing