The Coffeealyzer showed that 25 of the 55 observations in the control group drank coffee. It also showed that all 55 observations in the treatment group drank coffee like they were supposed to!

You discover that most of the coffee drinkers in the control group are working at least two different jobs. Previous research shows that those working more than one job, on average, are less productive at any of their jobs than those only working one job, all else equal.

To deal with the problem you discovered in the experiment, you decide to drop those in the control group that drank coffee from the study. After dropping these observations, the difference in averages will
[选择]
Overestimate
Be unbiased for
Underestimate
the ATT.

Question

The Coffeealyzer showed that 25 of the 55 observations in the control group drank coffee.  It also showed that all 55 observations in the treatment group drank coffee like they were supposed to!

You discover that most of the coffee drinkers in the control group are working at least two different jobs. Previous research shows that those working more than one job, on average, are less productive at any of their jobs than those only working one job, all else equal.

To deal with the problem you discovered in the experiment, you decide to drop those in the control group that drank coffee from the study.  After dropping these observations, the difference in averages will 
[选择]
Overestimate
Be unbiased for
Underestimate
 the ATT.

BlackTom AI · Accepted Answer

Question restatement and setup:
- We have an experiment comparing a control group and a treatment group. In the control group, 25 of 55 observations drank coffee. In the treatment group, all 55 observed drank coffee. You find that many coffee drinkers in the control group work at least two jobs, and prior research suggests multi-job workers are, on average, less productive. To address this, you drop coffee-drinkers from the control group. The resulting difference in averages will [选项]. The options are: Overestimate, Be unbiased for, Underestimate the ATT (average treatment effect on the treated).

Analysis of each option:
Option 1: Overestimate
- The key issue is that dropping coffee drinkers in the control group removes a subset of control observations with systematically different characteristics (more multi-job workers and potentially lower productivity).
- By removing these lower-productivity individuals from the control group, the remaining control group becomes relatively higher in productivity on average, reducing the difference between treatment and control groups compared to the true population difference.
- Since the treatment group already has all individuals drinking coffee (and presumably similar work patterns), dropping the lower-productivity coffee-drinkers from the control inflates the apparent effect of the treatment. You would expect the estimated ATT to be larger in magnitude than the true ATT, i.e., an overestimate.
- This reasoning relies on the assumption that the dropout mechanism is related to both treatment status and the outcome (productivity), i.e., a form of selection bias that biases the estimate upward.

Option 2: Be unbiased for the ATT
- Achieving an unbiased ATT would require that the control group, after dropping certain observations, remains representative of the same underlying population as the treated group, or that the dropout mechanism is ignorable with respect to the potential outcomes.
- In this scenario, dropping coffee-drinkers who are more likely to be multi-job workers introduces a nonrandom selection that is correlated with productivity, violating the ignorability condition.
- Therefore, the resulting estimate is unlikely to be unbiased for the ATT, because the control group is no longer representative of what would have happened to similar individuals had they not been treated.

Option 3: Underestimate
- An underestimation would mean the difference in averages after dropping coffee-drinkers would shrink relative to the true ATT.
- Given that you removed lower-productivity control observations (coffee drinkers who also work multiple jobs), the control group’s average productivity increases, which would inflate the difference, not shrink it. This makes underestimation less plausible.
- The mechanism described tends to push the estimate upward (toward a larger positive ATT) rather than downward.

Option 4: (If present) any other option would need to align with the same reasoning about selection bias and changes to the control group composition. Since the only specified candidates are Overestimate, Be unbiased for, and Underestimate, the core intuition is that removing a biased subset from the control group tends to exaggerate the treatment effect rather than neutralize it or shrink it.

Synthesis of reasoning across options:
- The core concept is that deleting a nonrandom, potentially productivity-affecting subset from the control group induces selection bias. Because those removed controls differ systematically from the remainder (more likely to be multi-job workers and less productive), the control mean shifts upward, widening the gap between treatment and control. This makes the estimated ATT larger than the true effect, i.e., an overestimate.
- The alternative that the estimate would be unbiased rests on strong assumptions about the dropout mechanism that are not satisfied here, making that option unlikely. The notion of underestimating runs counter to the expected direction given the removal of lower-performing controls, so it is also unlikely.
- If an additional option existed that assumed a more nuanced adjustment (e.g., using weighting or matching to restore balance), that might be plausible, but within the given choices, the dominant bias direction is toward overestimation.

Overall takeaway:
- The elimination of a systematically different subset from the control group (coffee drinkers who are more likely to juggle multiple jobs) tends to increase the observed treatment effect, pointing toward an overestimate of the ATT. This aligns with standard selection-bias intuition in causal inference when nonrandom dropout or exclusion alters the comparability of groups.

FA25_QTM_110_1 Quiz #6: Internal and External Validity of Randomized Experiments

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