Aria Cederlof, Kepuali Otuafi, Addison Scanlon, and Kenan Ince
November 21, 2021
We used a \( \chi^{2} \) model with \( 4-1=3 \) degrees of freedom. The three conditions that must be checked are:
# A tibble: 1 × 4
statistic p.value parameter method
<dbl> <dbl> <dbl> <chr>
1 2237. 0 3 Chi-squared test for given probabilities
The value of our 2014 \( \chi^{2} \) is 2237.4214612 with a \( p \)-value of less than \( 0.0001 \). We reject the null hypothesis of no difference in racial demographics. There is statistically significant evidence that the distribution of races against whom SLCPD used force is different from the distribution of races in Salt Lake City.
The residuals show the difference between our observed and expected counts. Negative numbers show underrepresentation, while positive numbers represent overrepresentation.
The farther the number is from 0, the more over/underrepresented a group is in our data. Residuals show a relative distance between the observed and expected values.
African Americans and Indigenous folks (coded as American Indians/Alaska Natives in the dataset) were overrepresented compared to their proportion in the population (thirty-four and twenty-seven more instances than expected). Asians were fairly underrepresented, with sixteen fewer instances than expected.
race_2014
Asian or Pacific Islander Black Indigenous
-16.033295 34.054482 27.916891
White
-6.426069
# A tibble: 1 × 4
statistic p.value parameter method
<dbl> <dbl> <dbl> <chr>
1 3196. 0 3 Chi-squared test for given probabilities
The value of our \( \chi^{2} \) is 3196.2268752. The \( p \)-value is less than \( 0.001 \). We reject the null hypothesis of no discrimination.
We may have made a Type I error, rejecting the null hypothesis when the null hypothesis was in fact true. This would mean that there really was no difference in the proportion of races, and that the observed overrepresentation of Black and Indigenous people of color in the use of force dataset was due to chance.
The value of our \( \chi^{2} \) is 46.7187277. The \( p \)-value is 3.9889362 × 10-10.
The p-value calculated is exceptionally small, meaning that we reject the null in favor of the alternative hypothesis. This means that there is significant evidence that the proportions of races in our data is not equal to the model proportions in the American Community Survey.
The value of our \( \chi^{2} \) is 857.9825016. The \( p \)-value is 1.1498775 × 10-185.
The p-value calculated is exceptionally small, meaning that we reject the null in favor of the alternative hypothesis. This means that there is significant evidence that the proportions of races in our data is not equal to the model proportions in the American Community Survey.
Any questions?