Question

Racism, juries, and interactions: In a study of racism, Nail, Harton and Decker (2003) had participants read a scenario in which a police officer assaulted a motorist. Half the participants read about an African American officer who assaulted an European American motorist, and half read about a European American officer who assaulted an African American motorist. Participants were categorized based on political orientation: liberal, moderate, or conservative. Participants were told that the officer was acquitted on assault charges in state court but found guilty of violating the motorist’s rights in federal court. Double jeopardy occurs when an individual is tried twice for the same crime. Participants were asked to rate, on a scale of 1-7, the degree to which the officer had been placed in double jeopardy by the second trial. The researchers reported the interaction as F= (2,58)=10.93, p<0.0001. The means for the liberal participants were 3.18 for those who read about the African American officer and 1.91 for those who read about the European American officer. The mean for the moderate participants were 3.50 for those who read about the African American officer and 3.33 for those who read about the European American officer. The means for the conservative participants were 1.25 for those who read about the African American officer and 4.62 for those who read about the European American officer.

a. Draw a table of cell means that includes that actual means for this study.

b. Do the reported statistics indicate that there is a significant interaction? If yes, describe the interaction in your own words.

c. Draw a bar graph that depicts the interaction. Include lines that connect the tops of the bars and show the pattern of the interaction.

d. Is this quantitative or qualitative interaction? Explain

e. Change the cell mean for the conservative participants who read about an African American officer so that this is now a quantitative interaction.

f. Draw a bar graph that depicts the patter that includes the new cell means

g. Change the cell means for the moderate and conservative participants who reads about an African American officer so that there is now no interaction.

h. Draw a bar graph that depicts the pattern that includes the new cell means.

Answer 1

a)

		Race
		African American	European American
Jury	Liberal	3.18	1.91
	Moderate	3.5	3.33
	Conservative	1.25	4.62

b)

The F-statistic for the test is,

Since the P-value for the F-statisitic is less than 0.05 at 5% significance level, there is a significant interaction exist between race and jurism.

c)

The charts are obtained in excel,

The parallel plot shows no interaction while non parallel plot shows interaction between two groups. From the line chart we can see that, the line for liberal and moderate influnced participants is roughly parallel and the line between moderate and and conservative particiapants is not parallel hence there is a interaction between these three type of particiapants.

d)

This is a qualitative interaction because the the direction of the line differs for at least one level of the factor.

( Qualitative interaction = when both the magnitude and direction of a variable changes with other variable, Quantitative interaction = when only the magnitude of a variable changes with other variable while the direction remain same, )

e)

Now changing the conservative participants who read about an African American officer from 1.25 to 4.

		Race
		African American	European American
Jury	Liberal	3.18	1.91
	Moderate	3.5	3.33
	Conservative	3.8	4.62

f)

g)

No interaction => parallel plot => difference between between the bar same (

		Race
		African American	European American	Difference
Jury	Liberal	3.18	1.91	1.27
	Moderate	4.6	3.33	1.27
	Conservative	5.89	4.62	1.27

h)