Chapter 11 - Interpreting the causal treatment effect #470
Description
There is an issue on chapter 11, in the following paragraph:
"Simply comparing those with and without the intervention, we can see that the treated have an achievement score that is, on average, 0.3185 (0.4723 - 0.1538) higher than the average score (which is zero, since the score is standardized)."
The average assessment score of those in the control group is not 0, but rather - 0.1538. As such, the average achievement score of those in the treatment group are 0.3185 higher than those in the control group.
The author presupposes that the mean test score of those in the control group have a average test score of 0 because the test is standardized. Test scores are typically standardized unconditionally, i.e. not conditioning on treatment status. The actual details of the data generating process are not included in the book. As such, the average assessment score of those in the control group is not 0 but the estimated coefficient on the intercept. The regression is incorrectly interpreted. If it truly was the case that the average test assessment scores of students in the control group was zero, you could have just excluded the intercept in the model - but here, you would be "forcing" the line of best to be go through the origin.