Technical Report
Vivienne Maxwell
1/24/2021
I. Introduction
The Corona Virus is not the only pandemic that the United States has experienced recently. Systemic racism and police brutality were brought to the nations’ attention this past summer at the height of quarantine. The murder of George Floyd prompted thousands of protesters to take to the streets, despite the hard lockdown and curfew that were put in place in an attempt to curb the spread of the virus.
With fatal police shootings on the rise (source: Statista), I was curious to see whether a general sense of discomfort and distrust in the police force had developed among individuals. According to Statista, Black Americans are killed at a much higher rate than other ethnicities, so clearly police brutality is race-related.
In response to the killings, the acronym ACAB (All Cops are B******) gained widespread popularity. I wanted to study whether all cops were perceived as equally threatening, or whether cops of a certain race and sex were perceived as more threatening than others.
In order to test this question, I decided to focus on two factors with two levels each:
Race (Black and White)
Sex (Male and Female)
My three hypotheses were that people would be more likely to distrust and feel uncomfortable around white police officers and male police officers, and that people would be most likely to distrust and feel uncomfortable around white male police officers.
II. Methods
In order to study popular sentiment in regards to police officers, a Randomized Basic Factorial (RBF[2]) study was designed. A survey using Qualtrics was created in which each factor (race and sex) was crossed. An image depicting one of the following four conditions (White Male cop, White Female cop, Black Male cop, and Black Female cop) was randomly assigned to a participant. The participant was then asked to rate their emotional responses to the image on a scale of disagree-agree. The three follow-up questions were:
I feel comfortable
I trust this individual to protect me
I would ask this individual for help
All participants had the same follow-up questions.
Mock Survey
One of the following conditions was randomly assigned to a participant. All of the participants were then asked to rank their emotional responses.
Fig.1: Image of a White Male police officer
Fig. 2: Image of a White Female police officer
Fig.3: Image of a Black Male police officer
Fig. 4: Image of a Black Female police officer
Fig. 5: Screenshot of how participants were asked to rank their emotional responses
III. Results
Comfort Level
The following figure illustrates how a police officer’s race and sex affects an individual’s level of comfort.
It appears that individuals tend to feel less comfortable around white male cops. However, it order to determine whether these trends are statistically significant, an Analysis of Variance (ANOVA) test is needed. It is also important to make note of the several outliers present in this data.
ANOVA
After checking that all of the Fisher Assumptions were met, an ANOVA test was conducted.
ANOVA Hypotheses for Comfort Levels
\(H_0:\) The Interaction between Race and Sex does not affect whether an individual feels comfortable
\(H_A:\) The Interaction between Race and Sex is a significant predictor of whether an individual feels comfortable
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| race | 1 | 12.8640897 | 12.8640897 | 10.0938320 | 0.0024212 |
| sex | 1 | 0.5352341 | 0.5352341 | 0.4199724 | 0.5195992 |
| race:sex | 1 | 3.4147788 | 3.4147788 | 2.6794125 | 0.1072614 |
| Residuals | 56 | 71.3692308 | 1.2744505 | NA | NA |
The ANOVA output suggests that the interaction between race and sex is not statistically significant (p=0.1). Therefore, we fail to reject the null hypothesis and cannot conclude that a police officer’s race and sex will predict how comfortable an individual feels. It is interesting to note that the predictor race is statistically significant (p=0.002). While the interaction between a police officer’s race and sex might not directly affect an individual’s comfort level, the race of an officer alone might have an effect.
Trust in Officer’s Protection
The following figure illustrates how a police officer’s race and sex affects whether an individual trusts that officer to protect them.
It appears that people trust black male cops to protect them more than white male cops. However, to determine whether these trends are statistically significant an Analysis of Variance test is needed. It is important to make note of the singular outlier for the black male cop.
ANOVA
After confirming the Fisher Assumptions were met, an ANOVA test was conducted.
ANOVA Hypotheses for Trust Levels
\(H_0:\) The interaction between the race and sex of a police officer does not determine whether an individual trusts them to protect them
\(H_A:\) The interaction between the race and sex of a police officer determines whether an individual trusts them to protect them
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| sex | 1 | 0.1853912 | 0.1853912 | 0.1718047 | 0.6800964 |
| race | 1 | 5.1684523 | 5.1684523 | 4.7896805 | 0.0328178 |
| sex:race | 1 | 3.5509642 | 3.5509642 | 3.2907306 | 0.0750307 |
| Residuals | 56 | 60.4285256 | 1.0790808 | NA | NA |
Looking at the ANOVA output, it appears that the interaction between race and sex is not statistically significant (p=0.07). Therefore, we fail to reject the null hypothesis and cannot conclude that a police officer’s race and sex determines whether an individual trusts them to protect them. Similar to the previous ANOVA test, the predictor race appears to be statistically significant (p=0.03). So while the interaction between race and sex of a police officer is not a significant predictor of trust, race alone might be.
Ask An Officer for Help
The following figure illustrates how likely an individual would ask a police officer for help depending on the police officer’s race and sex.
This figure is interesting. All of the medians are centered on “Agree”, however the distribution for each condition varies widely. It appears that individuals would be more likely to ask black male cops for help and would be less likely to ask white male cops for help. In order to determine whether these trends are statistically significant, an Analysis of Variance (ANOVA) test must be done. There is another outlier present for the black male cop.
ANOVA
After checking that the Fisher Assumptions were met, ANOVA was conducted.
ANOVA Hypotheses for Asking for Help
\(H_0:\) The interaction between a police officer’s race and sex does not determine whether an individual will ask that officer for help.
\(H_A:\) The interaction between a police officer’s race and sex does determine whether an individual will ask that officer for help.
| Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| sex | 1 | 0.3230256 | 0.3230256 | 0.2365296 | 0.6286219 |
| race | 1 | 2.9657423 | 2.9657423 | 2.1716105 | 0.1461783 |
| sex:race | 1 | 1.8327065 | 1.8327065 | 1.3419657 | 0.2516041 |
| Residuals | 56 | 76.4785256 | 1.3656880 | NA | NA |
The ANOVA output suggests that the interaction between race and sex is not statistically significant (p=0.25). We therefore will reject the null hypothesis and cannot conclude that the interaction between a police officer’s race and sex will determine whether an individual will ask that officer for help. This ANOVA output differs from the other two, in that in previous analyses the predictor race was statistically significant. In this case, race is not statistically significant (p=0.1), so we cannot conclude that either race alone or the interaction between race and sex will influence whether an individual will ask an officer for help.
IV. Conclusion
The aim of this Randomized Basic Factorial 2 experiment was to test whether a general sense of discomfort and distrust had developed against cops, and whether all cops were perceived as equally threatening. The three questions were designed to better understand people’s emotional responses to the police force, testing for comfort, trust, and whether individuals would ask an officer for help.
After analyzing and visualizing the data, some interesting trends were made apparent. It appears that overall, people tend to feel less comfortable around white male cops, neither trust nor distrust white male officers to protect them, and might ask a white male officer for help though the data skew towards not asking for help.
The ANOVA results tell us that while the trends are interesting, they are not statistically significant. The interaction between race and sex for all three questions was not statistically significant. However, for comfort level and trust levels, the predictor race was statistically significant, so it could be that race alone has some effect.
Limitations
Overall, there were several limitations to this study. There were only 60 survey responses, which is not a large sample size. The sampled individuals were not completely random; the majority of participants were students of the SDS 290 course as well as personal acquaintances. The survey was anonymous so there is no information regarding the participants’ race or ethnicity. In future studies that would be something to consider taking into account, as it could be that individuals of one race or ethnicity feel more or less threatened by the police than individuals of another race or ethnicity.
While all of the findings presented in this study are statistically insignificant and cannot be used to make causal claims, it does bring forth an interesting perspective and illuminate interesting trends. Hopefully, as Covid vaccines become more widepread and the pandemic runs its course, so will systemic racism and police brutality.
V. Appendix
Fisher Assumptions
Comfort
The histogram of the residuals appears to follow a slightly normal distribution and for the sake of this exercise we will assume the condition of normality is met.
The normal Q-Q Plot looks fairly linear, and we will therefore assume the condition of normality is met.
| race | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| female.black | 1 | 1.00 | 2.0 | 3 | 4 | 2.307692 | 1.2506409 | 13 | 0 |
| male.black | 1 | 1.75 | 2.0 | 2 | 4 | 2.000000 | 0.8164966 | 16 | 0 |
| female.white | 1 | 2.00 | 2.5 | 3 | 5 | 2.750000 | 1.1254629 | 16 | 0 |
| male.white | 1 | 2.00 | 4.0 | 4 | 5 | 3.400000 | 1.2983506 | 15 | 0 |
| black | 1 | 1.00 | 2.0 | 3 | 4 | 2.137931 | 1.0255360 | 29 | 0 |
| white | 1 | 2.00 | 3.0 | 4 | 5 | 3.064516 | 1.2365404 | 31 | 0 |
We can assume that the condition of equal variance is met as none of the standard deviations are three times larger than one another other.
Trust in Officer’s Protection
The histogram of the residuals appears to follow a normal distribution pattern, so we can conclude that condition of normality is met.
Similarly, the Normal Q-Q plot of the residuals follows a relatively straight line, so we can conclude that the condition of normality has been met.
| race | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| female.black | 1 | 1 | 3 | 3.0 | 4 | 2.230769 | 1.2351684 | 13 | 0 |
| male.black | 1 | 1 | 2 | 2.0 | 4 | 1.875000 | 0.8062258 | 16 | 0 |
| female.white | 1 | 2 | 2 | 3.0 | 4 | 2.312500 | 0.9464847 | 16 | 0 |
| male.white | 1 | 2 | 3 | 3.5 | 5 | 2.933333 | 1.1629192 | 15 | 0 |
| black | 1 | 1 | 2 | 3.0 | 4 | 2.034483 | 1.0170953 | 29 | 0 |
| white | 1 | 2 | 2 | 3.0 | 5 | 2.612903 | 1.0855849 | 31 | 0 |
We can conclude that the condition of equal variance is met, as all of the standard deviations are well within range.
Asking an Officer for Help
The histogram of the residuals appears to follow a fairly normal distribution pattern though the data appear to be slightly right skewed. For the sake of this exercise we will assume that the condition of normality has been met.
The Normal Q-Q Plot for these residuals appear to be relatively linear, therefore we will assume the condition of normality has been met.
| race | min | Q1 | median | Q3 | max | mean | sd | n | missing |
|---|---|---|---|---|---|---|---|---|---|
| female.black | 1 | 1.00 | 2 | 3.0 | 4 | 2.230769 | 1.2351684 | 13 | 0 |
| male.black | 1 | 1.00 | 2 | 2.0 | 4 | 1.750000 | 0.8563488 | 16 | 0 |
| female.white | 1 | 1.75 | 2 | 3.0 | 4 | 2.312500 | 1.0781929 | 16 | 0 |
| male.white | 1 | 1.50 | 2 | 4.0 | 5 | 2.533333 | 1.4573296 | 15 | 0 |
| black | 1 | 1.00 | 2 | 2.0 | 4 | 1.965517 | 1.0516232 | 29 | 0 |
| white | 1 | 1.50 | 2 | 3.5 | 5 | 2.419355 | 1.2589465 | 31 | 0 |
All of the standard deviations are within range, so the condition of equal variance is met.
Citations
Statista Research Department. “People Shot to Death by U.S. Police, by Race 2020.” Statista, 5 Jan. 2021, www.statista.com/statistics/585152/people-shot-to-death-by-us-police-by-race/.
Figure 1: Dennis, Marian. “Spring City Welcomes New Police Chief.” The Pottstown Mercury, 14 Sept. 2018, www.pottsmerc.com/news/spring-city-welcomes-new-police-chief/article_be82e9ba-b81d-11e8-9c92-278fa53b4dc3.html.
Figure 2: Loeks, Maunette. “Scottsbluff Officer Krisa Brass Climbs in Her Career, but Sees Challenges as a Woman Officer.” Starherald.com, 26 Oct. 2020, starherald.com/news/local/crime-and-courts/scottsbluff-officer-krisa-brass-climbs-in-her-career-but-sees-challenges-as-a-woman-officer/article_45c0d282-359c-5389-b913-988ef48d7dbb.html.
Figure 3: Curnette, Mark. “Black Police Group Unhappy with Political Endorsements.” Cincinnati.com, 16 Oct. 2016, www.cincinnati.com/story/news/politics/elections/2016/10/20/black-police-group-unhappy-political-endorsements/92467550/.
Figure 4: “Joy-Jefferson-Police-Women-memphis2 (Black Belt or Not, I’d Be Afraid to Get into a Ring with JOY JEFFERSON!).: Police Women, Female Cop, Female Police Officers.” Pinterest, www.pinterest.com/pin/529595237409450403/.