Robert Martin was laid off from his job at Westvaco, Inc. soon after he turned 55 years old. He sued for age discrimination. How do we evaluate his claim?
Ages of all employees in the department: 25, 33, 35, 38, 48, 55, 55, 55, 56, 64
Ages of the 3 employees who were fired: 55, 55, 64
We know which of the 10 people in this department got fired. And, we know they were older on average than the rest. But what we really want to know is: what is the Data Generating Process? Does age play a role in determining who gets fired, or could the apparent association between age and being fired be simply the result of random processes?
Now we can return to our two possible models of the DGP: 1. fired = age + other stuff 2. fired = other stuff We can simulate the second model. If we do that, we can then see how likely our actual data (e.g., the mean age of employees who were fired) would be to occur IF the second (completely random) model were true.
Let's use the sampling distribution to help us think about the alternative models of the DGP. How likely is it that we would have obtained and average age of 58 for fired employees if we had just fired people randomly?