Respondents who don’t pay attention or respond insincerely are in vogue (see the second half of the note). But how do you deal with such respondents in an experiment?

To set the context, a toy example. Say that you are running an experiment. And say that 10% of the respondents in a rush to complete the survey and get the payout don’t read the survey question that measures the dependent variable and respond randomly to it. In such cases, the treatment effect among the 10% will be centered around 0. And including the 10% would attenuate the Average Treatment Effect (ATE).

More formally, in the subject pool, there is an ATE that is E[Y(1)] – E[Y(0)]. You randomly assign folks, and under usual conditions, they render a random sample of Y(1) or Y(0), which in expectation retrieves the ATE. But when there is pure guessing, the guess by subject i is not centered around Y_i(1) in the treatment group or Y_i(0) in the control group. Instead, it is centered on some other value that is altogether unresponsive to treatment.

Now that we understand the consequences of inattention, how do we deal with it?

We could deal with inattentive responding under compliance, but it is useful to separate compliance with the treatment protocol, which can be just picking up the phone, from attention or sincerity with which the respondent responds to the dependent variables. On a survey experiment, compliance plausibly adequately covers both, but cases where treatment and measurement are de-coupled, e.g., happen at different times, it is vital to separate the two.

On survey experiments, I think it is reasonable to assume that:

- the proportion of people paying attention are the same across Control/Treatment group, and
- there is no correlation between who pays attention and assignment to the control group/treatment group, e.g., men are inattentive in the treatment group and women in the control group.

If the assumptions hold, then the worst we get is an estimate on the attentive subset (principal stratification). To get at ATE with the same research design (and if you measure attention pre-treatment), we can post-stratify after estimating the treatment effect on the attentive subset and then re-weight to account for the inattentive group. (One potential issue with the scheme is that variables used to stratify may have a fair bit of measurement error among inattentive respondents.)

The experimental way to get at attenuation would be to manipulate attention, e.g., via incentives, after the respondents have seen the treatment but before the DV measurement has begun. For instance, see this paper.

Attenuation is one thing, proper standard errors another. People responding randomly will also lead to fatter standard errors, not just because we have fewer respondents but because as Ed Haertel points out (in personal communication):

- “The variance of the random responses could be [in fact, very likely is: GS] different [from] the variances in the compliant groups.”
- Even “if the variance of the random responses was zero, we’d get noise because although the proportions of random responders in the T and C groups are equal in expectation, they will generally not be exactly the same in any given experiment.”