Pub Aff 60 Homework 4

Homework4 5/20/2021 Q1: H(0): b1 = 0 Q2: I expect the relationship between the years and the degree of racial bias stops to be positive and b2 to be greater than zero. H(2): b2 > 0 Q3: H(0): b2 = 0 Q4: Another confounding variable may be current events during the years in our study. For example, a recent terrorist attack may make cops more likely to stop individuals based on race, or a current rights movement (or stories in the news) could increase awareness causing cops to be more aware of their racial biases. There really would not be a way to measure this variable. It also depends on how many cops are exposed to the news. Perhaps if current events led to changes in regular trainings (whether frequency or subject matter), then those could either decrease or increase racial bias in police stops. load( file = "StopAndFrisk.RData" ) names(frisks) ## [1] "year" "tot_stop" "black" "white" ## [5] "numarr_blk" "numarr_wht" "offid_blk" "offid_wht" ## [9] "frisked_blk" "frisked_wht" "force_blk" "force_wht" ## [13] "tot_arr" "med_incNYC" "umemp_NYC" "ShareInc_1perc" frisks$recession <- 0 frisks$recession[frisks$year> 2008 & frisks$year<= 2012 ] <- 1 frisks$recession ## [1] 0 0 0 0 0 1 1 1 1 0 frisks$ratio_bw <- frisks$black / frisks$white Q5: If the ratio is greater than one in a particular year, that means more police stops occurred for black suspects than white suspects. If the ratio is less than one, that means there were more police stops for white suspects than black suspects. summary(frisks$ratio_bw) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 4.409 4.792 5.189 5.187 5.667 5.795 Q6: The lowest value observed was 4.409, while the highest was 5.795. This means that the ratio between stops for black suspects and stops for white suspects in our given time frame ranged between 4.409 and 5.795. hist(frisks$ratio_bw)

Q7: The distribution is unimodal and appears it may be skewed to the left. The modal range is 5.6-5.8. plot(frisks$year, frisks$ratio_bw, main = "" , xlab = "Year" , ylab = "Ratio Between Stops for Black to White Suspects" , pch = 19 )

## ## Call: ## lm(formula = ratio_bw ~ med_incNYC + recession + tot_stop, data = frisks) ## ## Residuals: ## Min 1Q Median 3Q Max ## -0.26253 -0.12441 0.02647 0.14304 0.18024 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 9.7620795 1.6190883 6.029 0.00094 *** ## med_incNYC -0.1222243 0.0399766 -3.057 0.02230 * ## recession 0.7401943 0.1901474 3.893 0.00805 ** ## tot_stop 0.0023576 0.0009506 2.480 0.04780 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.191 on 6 degrees of freedom ## Multiple R-squared: 0.9097, Adjusted R-squared: 0.8645 ## F-statistic: 20.14 on 3 and 6 DF, p-value: 0.001557 Q11: The p-value for our estimate on the relationship between median income and racial bias is 0.02230, meaning the result is statistically significant, assuming we are using a 0.05 alpha-level. It is not, however, statistically significant if using an alpha-level of 0.01. plot(test$coefficients[ 2 : 4 ], 1 : 3 , type = "n" , xlab = "Estimated Slope" , yaxt = "n" , ylab = "" , main = "Confidence Intervals" , xlim = c(- 0.3 , 1.2 )) par( las = 1 ) mtext( c( "Med Income" , "Recession" , "Tot Stops" ), side = 2 , at = c( 1 , 2 , 3 ), line = 0.5 , cex = 0.7 ) abline( v = 0 , col = "red" , lty = 2 ) stderrors <- summary(test)$coefficients[, 2 ] segments( x0 = test$coefficients[ 2 : 4 ]+ ( qnorm( 0.995 ) * stderrors[ 2 : 4 ] ), y0 = 1 : 3 , x1 = test$coefficients[ 2 : 4 ]+ ( qnorm( 0.005 ) * stderrors[ 2 : 4 ] ), y1 = 1 : 3 , col = "darkgray" ) segments( x0 = test$coefficients[ 2 : 4 ]+ ( qnorm( 0.95 ) * stderrors[ 2 : 4 ] ), y0 = 1 : 3 , x1 = test$coefficients[ 2 : 4 ]+ ( qnorm( 0.05 ) * stderrors[ 2 : 4 ] ), y1 = 1 : 3 ) points(test$coefficients[ 2 : 4 ], 1 : 3 , pch = 19 , cex = 0.7 )

lowerbound_rec <- test$coefficients[ 4 ]+ ( qnorm( 0.05 ) * stderrors[ 4 ] ) as.numeric(lowerbound_rec) ## [1] 0.0007939495 upperbound_rec <- test$coefficients[ 4 ]+ ( qnorm( 0.95 ) * stderrors[ 4 ] ) as.numeric(upperbound_rec) ## [1] 0.003921242 Q12: The estimated slope of the total stops variable is statistically significantly different from 0 at an alpha-level of 0.1. This confidence interval means that 90% of possible values for b3 when factoring in sampling variability fall between the two bounds given. b3 is the slope of the relationship between total stops and racial bias, and our null hypothesis for the total stops variable was that b3 = 0. Since the interval does not encompass zero, we can reject the null hypothesis. Q13: Based on the plot, the estimated slope between median income and racial bias is statistically significantly different from zero because the confidence interval does not overlap zero. This means we can reject the null hypothesis. Q14: The results are consistent with our H1 hypothesis because they are statistically significantly less than zero.

Q15: Looking at this plot, the estimated slope on recession is statistically significantly larger than 0.28 at an alpha-level of 0.1, but not at an alpha-level of 0.01. Q16: A correlation between our explanatory variables could be inconsistent with our argument but explain our results. We would have to conduct tests factoring variability for each variable based on the others. Q17: One limitation of the study is that we do not have very many years factored in here. Perhaps before 2003, the racial bias ratios were as high as they were during the recession, while not being caused by the recession. Q18: Some implications of our argument are that a worsened economy causes more racial bias in our law enforcement and that increased law enforcement causes increased racial bias in enforcement. There is not enough data to prove the causality of these casual claims, but possibly correlation.