1. Measures of association - Phi and Cramer's V

Please answer all 5 questions. The word bank is beside the question. Select an answer from the answers provided.

The U.S. Department of Justice collects data on involuntary citizen contacts with police, specifically those that occur when the person is the driver of a motor vehicle (that is, traffic stops) or when the person is stopped by the police while in a public place but not in a moving vehicle (that is, street stops). One item of interest is public perception of police behavior and police legitimacy during traffic and street stops.

Suppose you are involved in a related study that examines public perception of police behavior during traffic stops in your city. You survey 3,497 drivers who were stopped by police while operating a motor vehicle. You collect information about the enforcement action that was taken by the police (that is, whether the driver was ticketed) and on the driver's perception of police behavior during the stop. The results are shown in the following bivariate table. Note that the table includes the value of chi square for this data.

	Enforcement Action (X)
Driver's Opinion (Y)	Ticketed	Not Ticketed	TOTALS
Police behaved properly	1,427	1,559	2,986
Police did not behave properly	357	154	511
TOTALS	1,784	1,713	3,497
			Chi square = 84.86, df = 1, p < 0.001.

You are interested in the possible association between the type of enforcement and driver perception of police behavior. Since you have a 2 x 2 bivariate table with nominal-level variables, you decide to use phi to measure the association between these variables. Calculate phi for these data:

1. Phi = ________ (the answer is either 0.218, 0.003, 0.110, or 0.156)

2. The result indicates a ___________ ( the answer is either weak, strong, moderate) relationship between the type of enforcement and the perception of police behavior.

You also collect demographic information about the drivers in the survey. Consider the following table, showing driver age group by type of enforcement action:

	Driver Age (X)
Enforcement Action (Y)	16-24	25-44	45-64	65 or older	TOTALS
Ticket	428	357	446	553	1,784
Warning	241	220	210	378	1,049
No action	173	166	146	179	664
TOTALS	842	743	802	1,110	3,497
					Chi square = 25.99, df = 6, p < 0.001.

You are interested in the possible association between driver's age and type of enforcement action. Since this bivariate table is larger than 2 x 2, the measure phi is not appropriate. Instead, you use Cramr's V to assess the strength of the relationship. Calculate Cramr's V for this table. (Note: The value of chi square is provided for you in the table.)

3. Cramr's V = ___________ (the answer is either 0.086, 0.000. 0.061, or 0.004)

4. This result indicates a ____________ ( the answer is either weak, strong, moderate) relationship between driver's age and type of enforcement action.

5. Which of the following conclusions are valid from this analysis? (the answer is either A, B, C, or D and it can be more than one)

A. The age of a driver affects the enforcement decision of police at traffic stops.

B. There is a strong association between the type of enforcement action at traffic stops and driver perception of police behavior.

C. There is a weak association between the type of enforcement action at traffic stops and the age of the driver.

D. There is a moderate association between the type of enforcement action at traffic stops and driver perception of police behavior.

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