BIVARIATE/MULTIVARIATE DESCRIPTIVE STATISTICS

Displaying and analyzing the relationship between categorical variables

Using the “crosstabulation” technique

• Open file Position stress gender.sav or .xls• Variables

– Position on the police force• Values: Patrol officer, Sergeant

– Stress• Values: Low, High

• What is the hypothesis? (Guess)

Hypothesis

• Two-tailed (do not predict the direction of the relationship)– Changes in Position cause changes in Stress

• One-tailed (predict the direction of the relationship)– Higher ranking officers have more stress

Using cross-tabulation (“crosstabs”)

• Analyze|Descriptive statistics|Crosstabs• Place independent variable in columns• Place dependent variable in rows• Select “Cells” & check “column

percentages”• Optional: For the dependent variable, to

have the “L” row appear above the “H” row, select “Format” & check “descending”

Job Stress

Position on police force

Low

High

Total

Sergeant

86

30

116

Patrol Officer

24

60 84

Total 110 90 N= 200

Job Stress

Position on police force

Low

High

Sergeant

78% 33%

Patrol Officer

22% 67%

Total 100% 100%

Two-tailed hypothesis: as the level of the independent variable changes (from Patrol Officer to Sergeant), does the distribution of the dependent variable change?

One-tailed hypothesis: Is this change in the hypothesized direction?

Introducing a “control” variable

• Could the apparent effect of position on stress actually be caused by another independent variable?

• Perhaps it’s “Gender” (M/F)– To challenge the opinion that Position affects Stress,

must choose a variable that is probably related to Position

– Gender is probably related to Position• In SPSS, add “Gender” to “Layer”

Job Stress

Position on police force

Low

High

Sergeant

70% 53%

Patrol Officer

30% 47%

Total 100% 100%

Job Stress

Position on police force

Low

High

Sergeant

83% 23%

Patrol Officer

17% 77%

Total 100% 100%

Females

Males

“First-order” Partial Tables

Does the original, “zero-order” relationship between variables still hold true for the Male value of the control variable? For the Female value?

Job Stress

Position on police force: Males

Low

High

Sergeant

83% 23%

Patrol Officer

17% 77%

Total 100% 100%

Job Stress

Position on police force: Females

Low

High

Sergeant

70% 53%

Patrol Officer

30% 47%

Total 100% 100%

Ethnicity

Support for police

Black

White

Total

Supportive

5

20

25

Neutral

15

5

20

Unsupportive

10

5

15

Total

30

30

N = 60

Ethnicity

Support for police

Black

White

Total

Supportive

Neutral

Unsupportive

Total

Insert percentages…

Ethnicity support for police

Ethnicity

Support for police

Black

White

Total

Supportive

5

20

25

Neutral

15

5

20

Unsupportive

10

5

15

Total

30

30

N = 60

Ethnicity

Support for police

Black

White

Total

Supportive

17%

66%

Neutral

50%

17%

Unsupportive

33%

17%

Total

100%

100%

Ethnicity support for police

Support for police

Black

White

Supportive

5

9

Neutral

10

3

Unsupportive

3

3

Total

18

15

Support for police

Black

White

Supportive

0

11

Neutral

5

2

Unsupportive

7

2

Total

12

15

Has Reported a Crime Never Reported a Crime

First-order partial tables

Control variable: prior report as a crime victim

Insert percentages…

Support for police

Black

White

Supportive

27%

60%

Neutral

56%

20%

Unsupportive

17%

20%

Total

100%

100%

Support for police

Black

White

Supportive

0%

74%

Neutral

42%

13%

Unsupportive

58%

13%

Total

100%

100%

Has Reported a Crime Never Reported a Crime

First-order partial tables

Control variable: prior report as a crime victim

First-order partial tables Reported a crime Never Reported a Crime

Zero-order table

Control variable: prior report as a crime victim

Hypothesis: Ethnicity determines support for police