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The Essentials of Statistics: A Tool for Social Research

Joseph F. Healey

Chapter 12

Association Between Variables Measured at the Ordinal Level - all with Video Answers

Educators


Chapter Questions

04:38

Problem 1

SOC A small sample of non-English-speaking immigrants to the United States has been interviewed about their level of assimilation. Is the pattern of adjustment affected by length of residence in the United States? For each table, compute gamma and summarize the relationship in terms of strength and direction. (HINT: $\operatorname{In} 2 \times 2$ tables, only two cells can contribute to $N_{s}$ or $N_{d}$ To compute $N_{s^{\prime}}$ multiply the number of cases in the upper left-hand cell by the number of cases in the lower right-hand cell. For $N_{d}$ multiply the number of cases in the upper righthand cell by the number of cases in the lower lefthand cell.
a. Facility in English:

Joseph Lentino
Joseph Lentino
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Problem 2

Compute gamma for the table presented in problem $11.1$ and reproduced below. Compare gamma with the nominal measure of association you computed in Chapter $11 .$ Are they similar in value? Do they characterize the strength for the association in the same way? What information about the relationship does gamma provide that is not available from nominal measures of association?

Victor Salazar
Victor Salazar
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04:09

Problem 3

CJ A sample of 150 cities has been classified as small, medium, or large by population and as high or low on crime rate. Is there a relationship between city size and crime rate? Describe the strength and direction of the relationship.

Raymond Matshanda
Raymond Matshanda
Numerade Educator
01:45

Problem 4

SOC Some researchers have argued that families vary by how they socialize their children to sports, games, and other leisure-time activities. In middleclass families, such activities are carefully monitored by parents and are, in general, dominated by adults (for example, Little League baseball). In workingclass families, children more often organize and initiate such activities themselves, and parents are much less involved (for example, sandlot or playground baseball games). Are the following data consistent with the ideas presented by the researchers? Summarize your conclusions in a few sentences.

James Kiss
James Kiss
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01:39

Problem 5

Is there a relationship between age and support for traditional gender roles? Is the relationship between the variables different for different nations? The World Values Survey has been administered to random samples drawn from Canada, the United States, and Mexico. Respondents were asked if they agree or disagree that a university education is more important for boys than for girls. Compute column percentages and gamma for each table. Is there a relationship? Describe the strength and direction of the relationship. Which age group is most supportive of traditional gender roles (agrees with the statement). How does the relationship change from nation to nation?

Sheryl Ezze
Sheryl Ezze
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Problem 6

PA All applicants to the local police academy are given an aptitude test, but the test has never been evaluated to see if test scores are in any way related to job performance. The following table reports aptitude test scores and job performance ratings for a sample of 78 policemen.
\begin{tabular}{lcccc}
\hline Efficiency & \multicolumn{3}{c} { Test Scores } & \\
\cline { 2 - 4 } Ratings & Low & Moderate & High & Totals \\
\hline Low & 12 & 6 & 7 & 25 \\
Moderate & 9 & 11 & 9 & 29 \\
High & 5 & $\frac{9}{26}$ & $\frac{10}{26}$ & $\frac{24}{78}$ \\
Totals & $\frac{56}{26}$ & 26 & 26 & 78 \\
\hline
\end{tabular}
a. Are these two variables associated? Describe the strength and direction of the relationship in a sentence or two.
b. Should the aptitude test continue to be administered? Why or why not?

Rashmi Sinha
Rashmi Sinha
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Problem 6

PA All applicants to the local police academy are given an aptitude test, but the test has never been evaluated to see if test scores are in any way related to job performance. The following table reports aptitude test scores and job performance ratings for a sample of 78 policemen.
\begin{tabular}{lcccc}
\hline Efficiency & \multicolumn{3}{c} { Test Scores } & \\
\cline { 2 - 4 } Ratings & Low & Moderate & High & Totals \\
\hline Low & 12 & 6 & 7 & 25 \\
Moderate & 9 & 11 & 9 & 29 \\
High & 5 & $\frac{9}{26}$ & $\frac{10}{26}$ & $\frac{24}{78}$ \\
\hline Totals & $\frac{5}{26}$ & 26 & 26 & 78 \\
\hline
\end{tabular}
a. Are these two variables associated? Describe the strength and direction of the relationship in a sentence or two.
b. Should the aptitude test continue to be administered? Why or why not?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:53

Problem 7

SW A sample of children has been observed and rated for symptoms of depression. Their parents have been rated for authoritarianism. Is there any relationship between these variables? Write a few sentences stating your conclusions.

EE
Elizabeth Edge
Numerade Educator
02:53

Problem 7

SW A sample of children has been observed and rated for symptoms of depression. Their parents have been rated for authoritarianism. Is there any relationship between these variables? Write a few sentences stating your conclusions.

EE
Elizabeth Edge
Numerade Educator
01:00

Problem 8

SOC Are prejudice and level of education related? State your conclusion in a few sentences.

Emily Himsel
Emily Himsel
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01:00

Problem 8

SOC Are prejudice and level of education related? State your conclusion in a few sentences.

Emily Himsel
Emily Himsel
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01:31

Problem 9

SOC In a recent survey, a random sample of respondents was asked to indicate how happy they were with their situations in life. Are their responses related to income level? Describe the strength and direction of the relationship.

Nick Johnson
Nick Johnson
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02:06

Problem 10

SOC A random sample of 11 neighborhoods in Leonia, Illinois, has been rated by an urban sociologist on a "quality-of-life" scale (which includes measures of affluence, availability of medical care, and recreational facilities) and a social cohesion scale. The results are presented here in scores. Higher scores indicate higher "quality of life" and greater social cohesion. Are the variables associated? What is the strength and direction of the relationship? (Hint: Do not forget to square the value of Spearman's rho for a $P R E$ interpretation.)

Brandon Cleary
Brandon Cleary
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00:50

Problem 11

SW Several years ago, a job-training program began, and a team of social workers screened the candidates for suitability for employment. Now the screening process is being evaluated, and the actual work performance of a sample of hired candidates has been rated. Did the screening process work?

Nick Johnson
Nick Johnson
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07:24

Problem 12

SOC Following are the scores of a sample of 15 nations on a measure of ethnic diversity (the higher the number, the greater the diversity) and a measure of economic inequality (the higher the score, the greater the inequality). Are these variables related? Are ethnically diverse nations more economically unequal?

Lisa Stryjewski
Lisa Stryjewski
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07:16

Problem 13

Twenty ethnic, racial, or national groups were rated by a random sample of white and black students on a Social Distance Scale. Lower scores represent less social distance and less prejudice. How similar are these rankings?

Harsh Gadhiya
Harsh Gadhiya
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01:50

Problem 14

In problem $11.9$, we looked at the relationships between five dependent variables and sex. Now we will use income as an independent variable and assess its relationship with this same set of variables. For each table, calculate percentages and gamma. Describe the strength and direction of each relationship in a few sentences. Be careful in interpreting direction.

Jon Southam
Jon Southam
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