The Mean Square Difference (MSD) I calculated from the probabilities of age and race in the dataset provided a quantitative measure of disparity in the experiences of Black and White individuals with respect to police shootings.
I performed a Monte Carlo simulation to test the mean square difference (MSD) calculated from our dataset against random samples. First, I defined the MSD value that we calculated from our data. Then, I conducted 10,000 simulations where I randomly shuffled the age and race data. For each simulation, I calculated the probabilities for Black and White races similar to how we did with our original data.
In each simulation, I computed the ratio of probabilities for Black and White races and then calculated the MSD using this ratio. This process allowed me to create a distribution of MSD values based on random chance.
After running the simulations, I compared the MSD value we calculated from our dataset with the distribution of MSD values from the random samples. The comparison was done by computing a p-value, which represents the probability of observing an MSD value as extreme as ours, or even more extreme, under the null hypothesis that there is no difference between races.