The data on police shootings, obtained from the Washington Post, provides valuable insights into various aspects of these unfortunate events. But first lets begin by understanding some methods and what they do.
What is Logistic Regression?
Logistic regression is a statistical method for analysing datasets where the outcome variable is binary (e.g., 0/1, Yes/No, True/False). It predicts the probability that a given instance belongs to a particular category.
In our analysis of police shootings data, we used logistic regression to predict if an individual was armed based on several factors: age, gender, race, flee status, and signs of mental illness.
Logistic Regression on Predicting Armed Status: Using age, gender, race, flee status, and signs of mental illness as predictors, our model achieved an accuracy of 93%. However, it showed a strong bias towards predicting that individuals were armed, indicating that there is potential need for further refinement or balancing techniques.
Why not Linear Regression?
While linear regression predicts a continuous outcome, logistic regression predicts the probability of an event occurring. It ensures that the predicted probabilities are between 0 and 1 using the logistic function (or sigmoid function).
Results & Implications:
Our model achieved a high accuracy of 93%. However, its bias towards predicting that individuals were armed indicates a potential imbalance.
In real-world scenarios, it’s crucial not just to consider accuracy but also other metrics like precision, recall, and the F1-score. Especially in sensitive contexts like police shootings, false negatives or false positives can have serious implications.
Permutation Tests: Empirical Hypothesis Testing
Permutation tests are a non-parametric method to test hypotheses. By shuffling labels and recalculating the test statistic, we can estimate a p-value based on the proportion of reshuffled datasets that provide as extreme (or more extreme) results as the original observed data.
In our analysis, the permutation test indicated a significant relationship between race and the likelihood of being armed during a police encounter.
Hypothesis Testing with Permutation Tests: We used a permutation test to examine the relationship between race and being armed. Our p-value of approximately 0.0163 suggests a significant relationship.
