Response bias

Response bias lives in the answers, not in the sample. The right people were reached, they responded, and what they said leans away from the truth in a consistent direction. The usual causes are leading or confusing wording, a sensitive question asked without anonymity, an interviewer whose presence changes what people will say, and faulty recall. Because the lean sits in the instrument, a flawless random sample with a 100 percent response rate can still return a badly wrong number.

A coach asks each of her 200 athletes face to face whether they skipped a scheduled workout last month, and 18 say yes, a reported rate of $\frac{18}{200} = 0.09$. The same 200 athletes then answer the same question on an anonymous form, and 62 say yes, or $\frac{62}{200} = 0.31$. The gap of 0.22 cannot be sampling variability, because it is the same 200 people both times. It is a property of how the question was asked.

"The athletes lied, so the data are just noisy" packs two errors into one clause. Noise is symmetric and averages out across samples, while under-reporting an embarrassing behavior pushes every repetition of that survey the same way, which is exactly what makes it bias. Blaming the respondents also misplaces the repair. What differed between 0.09 and 0.31 was the format of the question, so that is where the fix belongs: neutral wording, anonymity, or a measurement that does not rely on self-report at all.

The direction is usually predictable. Socially approved behavior gets over-reported and disapproved behavior under-reported, so self-reported exercise and voting run high while self-reported drinking and cheating run low. A leading question pushes answers toward whatever it hints at. Naming which way, in the context of the study, is the half of the answer graders look for.

Two things response bias is not. It is not nonresponse bias, because everyone here answered. It is not undercoverage, because everyone here was reachable. It also survives a perfect sampling design, since fixing who ends up in the sample does nothing to the question those people are handed.