Deck 14: Association Between Variables Measured at the Ordinal Level

Question 1

Which measure of association is based on predicting the order of pairs of cases?

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

Answer 1

gamma

Question 2

Gamma will be zero if

A)the variables are strongly related.
B)the relationship is negative.
C)knowledge of the independent variable does not improve our ability to predict the dependent variable.
D)the scores of each case are symmetrical to the scores of all other cases.

Answer 2

knowledge of the independent variable does not improve our ability to predict the dependent variable.

Question 3

Gamma is an appropriate measure of association for

A)examining the relationships between more than two ordinal-level variables.
B)nominal-level variables with more than 3 scores.
C)ordinal level variables arranged in a bivariate table.
D)ordinal level variables with many scores.

Answer 3

ordinal level variables arranged in a bivariate table.

Question 4

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 5

For variables measured at the ordinal level,gamma measures

A)the statistical significance of the relationship.
B)the proportional reduction in error gained by predicting one variable while taking the other into account.
C)the relative importance of each variable to the association.
D)all of the above

Question 6

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 7

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 8

A researcher tested the relationship between occupational prestige and level of approval of a proposal to ban handguns in the state and found a gamma of -0.17.This relationship is

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

Question 9

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 10

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 11

The lowest possible value (indicating the weakest possible relationship)for gamma is

A)-1.00.
B)-10.00.
C)0.05.
D)0

Question 12

Gamma and lambda are based on the logic of

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

Question 13

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 14

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 15

Gamma ranges from

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

Question 16

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 17

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 18

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 19

A researcher tested the relationship between occupational prestige and level of approval of a proposal to ban handguns in the state and found a gamma of -0.17.This means that

A)as prestige goes up,support for the ban goes down.
B)the electorate will approve the ban.
C)support for the ban is highest among the rich.
D)support tends to increase as prestige increases.

Question 20

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 21

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 22

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 23

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 24

In the formula for gamma,N_d 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 25

A bivariate table has 1843 pairs of cases ranked the same (N_s)and 345 pairs of cases ranked differently (N_d).This is

A)a negative relationship.
B)a positive relationship.
C)a very weak relationship.
D)impossible.These totals are mathematically impossible.

Question 26

Table 14.1
$\begin{array}{|l|l|l|l|}\hline \text { Table 14.1 Support for }\\\text {Restrictive Immigration}\\ \text {Policy by Education}\\\hline & \text { EDUCATION}\\\hline \text { SUPPORT } & \text { Less than HighSchool } & \text { HighSchool } & \text { College } \\\hline \text { Low } & 60 & 30 & 10 \\\hline \text { Neutral } & 20 & 30 & 20 \\\hline \text { High } & 10& 40 & 70 \\\hline &100\%&100\%&100\%\\\hline\end{array}$
Table 14.1 shows a relationship between education and support for a policy to restrict immigration to the United States.The relationship between education and opposition is

A)positive.
B)negative.
C)neither a positive nor negative relationship since the variables are measured at the nominal level.
D)none of the above

Question 27

A bivariate table has 723 pairs of cases ranked the same (N_s)and 1489 pairs of cases ranked differently (N_d).This is

A)a negative relationship.
B)a positive relationship.
C)a very weak relationship.
D)impossible.These totals are mathematically impossible.

Question 28

According to research presented in the text,a gamma measuring the relationship between TV viewing and involvement was -0.11.This means that

A)heavy TV viewers are less likely to volunteer.
B)there is no relationship between these variables.
C)there is a very strong relationship between these variables.
D)heavy TV viewers are more involveD.

Question 29

Mathematically,gamma is the ratio of the difference between the number of pairs of cases ranked the same minus the number of pairs of cases ranked differently to

A)N.
B)Chi square.
C)the total number of pairs of cases (not counting ties).
D)1.00.

Question 30

According to the information reported in the text,the relationship between level of involvement in social life and amount of TV watching was

A)negative but statistically significant.
B)statistically significant,strong,and positive.
C)weak,negative,and statistically significant.
D)moderate,positive,but not significant.

Question 31

Gamma is a symmetrical measure of association.This means that

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

Question 32

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

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

Question 33

Although the relationships were weak,the research reported in the text showed that people who were more involved socially tended to be

A)part-time workers and single.
B)unmarried,full time workers,people who watch relatively little TV.
C)unmarried,part-time workers,heavy TV viewers.
D)unmarried women with high levels of education.

Question 34

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 35

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 36

Spearman's rho is appropriate for use with

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

Question 37

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 38

Table 14.1
$\begin{array}{|l|l|l|l|}\hline \text { Table 14.1 Support for }\\\text {Restrictive Immigration}\\ \text {Policy by Education}\\\hline & \text { EDUCATION}\\\hline \text { SUPPORT } & \text { Less than HighSchool } & \text { HighSchool } & \text { College } \\\hline \text { Low } & 60 & 30 & 10 \\\hline \text { Neutral } & 20 & 30 & 20 \\\hline \text { High } & 10& 40 & 70 \\\hline &100\%&100\%&100\%\\\hline\end{array}$
In Table 14.1,support for immigration restriction ____ as education increases.

A)decreases
B)increases
C)moderates
D)weakens

Question 39

In the logic of gamma,pairs of cases in the same row or column are

A)tied on both X and Y.
B)always have different scores.
C)are tied on at least one of the variables.
D)subtracted from the value of gamma.

Question 40

In the formula for gamma,N_s 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 41

Many studies have explored the relationship between smoking and health problems.If one of these studies found a Spearman's rho of +0.78 between amount of smoking and seriousness of health problems,this would indicate

A)that smoking causes health problems.
B)a positive,causal relationship between these variables.
C)a positive,strong relationship between these variables.
D)a positive,statistically significant relationship between these variables.

Question 42

Tests of significance based on gamma and Spearman's rho assume

A)random sampling.
B)ordinal level of measurement.
C)normal sampling distribution.
D)all of the above

Question 43

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 44

The null hypothesis for test of significance with gamma states that

A)there is no association between the variables in the sample.
B)there is a perfect association between the variables in the sample.
C)there is no association between the variables in the population from which the samples were taken.
D)chi square is zero.

Question 45

Is there an association between support for the legalization of marijuana and age? Calculate percentages and gamma for the table below and write a sentence or two assessing the strength and direction of the relationship.

Question 46

To establish the critical area under the sampling distribution for Spearman's rho,we use

A)the Z distribution.
B)the t distribution.
C)the chi square distribution.
D)the distribution of rho.

Question 47

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 48

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.

Question 49

To establish the critical area under the sampling distribution for gamma,we use

A)the Z distribution.
B)the t distribution.
C)the chi square distribution.
D)the gamma distribution.

Question 50

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 51

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 52

Scales have been administered to eleven individuals measuring their job satisfaction and the prestige 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.