Inference

With thanks to Allen Downey for his suggestions in inference in three hours.

In our answer for the Supreme Court, we discovered the process of statistical inference.

Statistical inference proceeds in these steps.

• Find the data. In our case, this was the race of the 12 people on Robert Swain’s jury, and the proportion of eligible voters who were Black.

• Calculate some measure of interest from the data. Call this the observed statistic. In our case, this was the number of Black jurors - 0.

• Make a simple model of the world to offer as an explanation of the data. This model is the null-world, also known as the null-hypothesis. In our case, the null-world was the model where the jurors were randomly selected from the eligible population.

• Simulate the data many times using the simple (null-world) model.

• For each simulation calculate the measure of interest. Call these the simulated measures. Our simulated measures were the number of black jurors in each simulation.

• Use the simulated measures to build up the sampling distribution.

• Compare the observed measure to the sampling distribution, to see whether it represents a rare or common event, given the model.