In situations where you know the individuals answering the survey are suspectible to some sort of bias within their responses, is there a way to simply integrate it into inferences made about the population? My initial thought is that some kind of adjusted confidence interval is the best place to do it.
A fictitous example:
I ask 100 individuals how much time they have spent on an activity in the past week (in minutes). I know from previous reports and research that when people are asked to re-collect time spent, they tend to under-estimate. On average, they under-estimate by about 20%.
Taking the responses direct from the 'survey' I get an average time of 100 minutes and a standard deviation of 25. From this I can create a standard confidence interval. But can I shift it and make it larger to account for the under-estimation?
A second fictitious example:
I ask 1000 individuals a sensitive question. 30% respond 'yes' and 70% respond 'no.' I know that those who answer 'yes' do not lie. However, of those who answer 'no', approximately 30% will lie.
I could take the responses directly from the survey and calculate a confidence interval for the percentage of individuals who would respond 'yes' in the population. But I want to incorporate the fact that some who answered 'no' would have lied. In which case, I almost have an asymmetric interval in which the true population parameter lies - it will have a wider interval above 30% than below.
P.S - I don't want to focus on how we can design surveys to avoid lying, bias etc.