Here’s a graph I want to insert in my book. It illustrates how to adjust for covariate imbalance. The data comes from the Data and Story Library
and shows the housing prices of 117 homes in Albuquerque, New Mexico in 1993. The data set also includes variables that might influence the sales price of the home such as the size in square feet, the age in years, and whether the house was custom built.
When you look at the average sales price for regular homes and custom built homes, you see a large discrepancy. Regular homes sell, on average for 95 thousand dollars, but custom built homes sell for 145 thousand dollars on average, a 50 thousand dollar discrepancy.
The trend line, though, show what happens when you adjust for size. The large gap shrinks by a considerable amount. There is still a significant difference in the prices, but not as extreme as the unadjusted values might lead you to believe.
You can find an earlier version of this page on my original website.