# How to resample members from the population who didn't respond after the survey?

I have used stratified random sampling on population to generate the sample. Now the issue is if after the survey is conducted some of the members in the sample didn't respond the survey and I would like to choose other memebers from the population (members to be selected from the same strata of people who didn't respond) so that the sample ratio of the variables are same as the population ratios.

I would like to know if there is any algorithm to do this in statistics. Also how to approach this issue so that I can get a representative sample of the population.

Any links and suggestions are appreciated. Thankyou!

• I think "resampling" here is being used with some loss of specificity - this is a sampling without replacement, you are merely trying to bolster your precision. If you really think subsequent methods are more likely to pressure people into the sample, you could consider inverse probability weighting. That is: assign the highest sampling weight to subjects least likely to be included in the sample. Apr 25 at 18:51
• Although there are algorithms, they don't address the underlying question, which concerns how nonrespondents might differ from respondents. The mere fact that some people don't respond strongly suggests some differences exist! Replacing them merely papers over that fundamental problem and can mislead people into thinking your results are more representative than they really are.
– whuber
Apr 25 at 22:54

In stratified random sampling we generally take a simple random sample of the desired size from each strata. In that case, if there are non-responses and you decide to sample additional people you would usually take a new simple random sample of the desired size from the subset of the strata that was not already sampled. You would do this for each strata.

The stratification and randomisation of the sampling are both designed to give a "representative sample" of the population, in a stochastic sense. So long as you use appropriate inference methods for your inferences about the population of interest, these sampling methods are quite good. As to algorithms for implementing simple random sampling, statistical software contains existing functions that can easily generate a simple random sample from a set of objects (e.g., see the sample function in R).

Of course, none of this fixes the inherent problem that non-respondents can differ systematically from respondents. Non-response in surveys is a significant source of bias in surveying work and it is inherently difficult to correct this using statistical inference methods, due to the lack of information about the non-respondent group. Consequently, most effort in surveying is directed to following up with non-respondents to see if the response rate can be increased.

• As @Ben says, this approach tends to work pretty well, but once you have nonresponse, you can't guarantee a representative survey. There may simply be a particular portion of the population who didn't respond to your survey and who, if included in this second sample, won't respond either. Apr 25 at 11:34
• +1 Such a replacement procedure can be really terrible. Imagine searching for buried treasure by drilling into the ground to look for gold in soil samples. Your sampling program calls for a grid search, with a spacing guaranteed to find a buried lockbox larger than a minimal size. Suppose your drill crew reported back and said "boss, there were several places we weren't able to drill because we hit something hard, so we just moved the drill a few feet over to get a replacement sample." How well do you think that would work? How accurately would your results reflect the reality? ;-)
– whuber
Apr 25 at 22:51
• Yes, true, but unfortunately sometimes the non-respondents are just that --- people who will not respond no matter how hard you try.
– Ben
Apr 25 at 22:53
• If the target of your inference is the population of people who do respond to surveys, no harm done. But if your target is the whole population, you're in trouble. (We're at risk of revisiting the US presidential election polling debacle of 2016...)
– whuber
Apr 25 at 22:55
• The target is usually the whole population, and non-response bias can be severe. I think it is important to get a completely random sample of the non-responders, and to incentivize them so that you get nearly all of the second phase random sample of subjects to respond. I wouldn't worry if they are not representative in terms of age or sex etc. That can be adjusted for with simple regression adjustment after the fact. Apr 25 at 23:05