*Notes Over Spring Break*

Midterms have been graded, and comments posted on Canvas. I would be happy to discuss the solutions with you in office hours or at a mutually convenient time. Here are two helpful pieces of information: the mean score on the test was \(\mu = 89.73\) (\(11.07\)), and the median score \(90.5\).

Replication papers are due at the end of the semester. We will now go around the room, please share the following details with the class: the paper you have shortlisted for replication, the key variables (outcome and treatment), whether or not replication data and code are available, and any extensions or limitations in the analysis you might have come across.

# Bias Due To Attrition

Missing outcome data (or attrition) is a threat to unbiased inference. This is because attrition jeopardizes the core assumptions of an experiment:

**De-randomization:** When missigness is systematically related to potential outcomes, the observed treatment or control group are no longer a random subset of the population. This implies that the treatment group mean is not an unbiased estimator of the population mean of \(Y_i(1)\):

#### \(E[\frac{\sum_{i=1}^m Y_i \cdot Z_i \cdot R_i}{\sum_{i=1}^m Z_i \cdot R_i}] \neq E[Y_i(1)]\)

and the control group mean is not an unbiased estimator of the population mean of \(Y_i(0)\):

#### \(E[\frac{\sum_{i=m+1}^N Y_i \cdot (1-Z_i) \cdot R_i}{\sum_{i=m+1}^N (1-Z_i) \cdot R_i}] \neq E[Y_i(0)]\)