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(Hypothetical data) Is a person’s race related to victimization? Suppose you hav

ID: 3220210 • Letter: #

Question

(Hypothetical data) Is a person’s race related to victimization? Suppose you have surveyed 30 people. You ask them:

Would you describe yourself as White (w) or Non-White (n)?

Would you describe yourself as Middle (m) or Working (w) Class?

Have you been a victim of a crime in the past year? (Yes = 1 or No = 0)

Case

Race

Class

Victim

N_times_vic

1

w

w

0

0

2

w

m

0

0

3

n

w

1

1

4

n

w

1

1

5

n

w

1

2

6

w

w

0

0

7

w

m

0

0

8

w

m

0

0

9

w

w

1

1

10

n

w

1

1

11

n

w

1

2

12

w

m

0

0

13

n

w

0

0

14

w

w

0

0

15

n

w

1

1

16

w

m

0

0

17

w

w

1

2

18

w

w

1

1

19

w

w

1

1

20

n

m

0

0

21

n

m

1

2

22

w

w

1

1

23

w

w

0

0

24

n

w

1

1

25

w

m

0

0

26

w

w

1

1

27

n

m

0

0

28

n

w

0

0

29

n

w

0

0

30

w

m

1

1

Construct a bivariate table of frequencies for race and victimization. Which is the independent variable?

Calculate percentages for the table based on the independent variable. Describe the relationship between race and victimization using the table.

Construct a bivariate table of frequencies for class and victimization. Which is the independent variable?

Calculate percentages for the table based on the independent variable. Describe the relationship between class and victimization using the table.

In the problem above, you examined racial and social class differences in victimization separately. You now wonder if the racial difference you found might be related to social class of the victim as well as his or her race.

Construct two bivariate tables: one table examining the victimization experience by race of those who are middle class and one table examining the victimization experience by race of those who are working class. Use percentages to illustrate differences by race, if any, between middle class and working class experience.

Interpret the results.

Case

Race

Class

Victim

N_times_vic

1

w

w

0

0

2

w

m

0

0

3

n

w

1

1

4

n

w

1

1

5

n

w

1

2

6

w

w

0

0

7

w

m

0

0

8

w

m

0

0

9

w

w

1

1

10

n

w

1

1

11

n

w

1

2

12

w

m

0

0

13

n

w

0

0

14

w

w

0

0

15

n

w

1

1

16

w

m

0

0

17

w

w

1

2

18

w

w

1

1

19

w

w

1

1

20

n

m

0

0

21

n

m

1

2

22

w

w

1

1

23

w

w

0

0

24

n

w

1

1

25

w

m

0

0

26

w

w

1

1

27

n

m

0

0

28

n

w

0

0

29

n

w

0

0

30

w

m

1

1

Explanation / Answer

Question 1

Construct a bivariate table of frequencies for race and victimization. Which is the independent variable?

Answer:

The bivariate table of frequencies for race and victimization is given as below:

Race * Victim Cross tabulation

Count

Victim

Total

No

Yes

Race

n

5

8

13

w

10

7

17

Total

15

15

30

For the above cross tabulation, the variables victim and race are independent.

Question 2

Calculate percentages for the table based on the independent variable. Describe the relationship between race and victimization using the table.

Solution:

The percentage table for the above cross tabulation is given as below:

Race * Victim Cross tabulation

Count

Victim

Total

No

Yes

Race

n

17%

27%

43%

w

33%

23%

57%

Total

50%

50%

100%

For checking the relationship between the race and victimization we have to use the chi square test for independence of two categorical variables. The test statistic formula is given as below:

Chi square = [(O – E)^2/E]

Where, O is the observed frequencies and E is the expected frequencies.

Expected frequencies = E = row total * column total / grand total

The calculation tables are given as below:

Observed Frequencies

Victim

Race

No

Yes

Total

N

5

8

13

W

10

7

17

Total

15

15

30

Expected Frequencies

Victim

Race

No

Yes

Total

N

6.5

6.5

13

W

8.5

8.5

17

Total

15

15

30

(O - E)

-1.5

1.5

1.5

-1.5

(O - E)^2/E

0.346153846

0.346153846

0.264705882

0.264705882

Level of Significance

0.05

Number of Rows

2

Number of Columns

2

Degrees of Freedom

1

Results

Critical Value

3.841459

Chi-Square Test Statistic

1.221719

p-Value

0.269024

Do not reject the null hypothesis

This means we conclude that there is sufficient evidence that there is no any association exists between the given two variables victim and race. The two categorical variables victim and race are independent from each other.

Question 3

Construct a bivariate table of frequencies for class and victimization. Which is the independent variable?

The bivariate table of frequencies for class and victimization is given as below:

Class * Victim Cross tabulation

Count

Victim

Total

No

Yes

Class

m

8

2

10

w

7

13

20

Total

15

15

30

Question 4

Calculate percentages for the table based on the independent variable. Describe the relationship between class and victimization using the table.

Class * Victim Cross tabulation

Count

Victim

Total

No

Yes

Class

m

27%

7%

33%

w

23%

43%

67%

Total

50%

50%

100%

For checking the relationship between the class and victimization we have to use the chi square test for independence of two categorical variables. The test statistic formula is given as below:

Chi square = [(O – E)^2/E]

Where, O is the observed frequencies and E is the expected frequencies.

Expected frequencies = E = row total * column total / grand total

The calculation tables are given as below:

Observed Frequencies

Victim

Class

No

Yes

Total

M

8

2

10

W

7

13

20

Total

15

15

30

Expected Frequencies

Victim

Class

No

Yes

Total

M

5

5

10

W

10

10

20

Total

15

15

30

(O - E)

3

-3

-3

3

(O - E)^2/E

1.8

1.8

0.9

0.9

Level of Significance

0.05

Number of Rows

2

Number of Columns

2

Degrees of Freedom

1

Results

Critical Value

3.841459

Chi-Square Test Statistic

5.4

p-Value

0.020137

Reject the null hypothesis

This means we conclude that there is sufficient evidence that there is an association exists between the given two variables victim and class. The two categorical variables victim and race are not independent from each other.

Race * Victim Cross tabulation

Count

Victim

Total

No

Yes

Race

n

5

8

13

w

10

7

17

Total

15

15

30