What you have is a subpopulation of individuals who would answer the survey. You also have a subpopulation of individuals that did not answer the survey. It is possible that these two subpopulations have very different responses. This is typically resolved by analyzing responses based on the number of times an individual had to be reminded. If there is no difference between response and number of reminders then one could argue that the non-responders are not significantly different than responders.

Hello James,

You attempted a census sample, and obtained a response rate of 60%. That's how you describe the method.

Could the result be biased? Yes.

What to do? Compare features of your sample to those that may be known for the entire population. For example, if you asked respondents to indicate their sex, age, or other personal characteristics, how closely do these align with what is true for the target population? You could test these for equality. To the extent that your sample appears to represent closely such features of the population, you might worry a little less about the possibility of a biased sample. No guarantees, however (this is true, by the way, even for a simple random sample in which you get 100% response from those selected).

Good luck with your work!

What you have is a subpopulation of individuals who would answer the survey. You also have a subpopulation of individuals that did not answer the survey. It is possible that these two subpopulations have very different responses. This is typically resolved by analyzing responses based on the number of times an individual had to be reminded. If there is no difference between response and number of reminders then one could argue that the non-responders are not significantly different than responders.

Dr. Ebert is quite correct and yes there is sampling error.. I would try to sample the nonresponse group again. Some will likely respond this time. Then there are various possibilities. you can pool the two samples and treat it as a big sample from the entire population. Don't forget to use the finite population correction factor (fpcf) where appropriate. A second alternative is to treat the two samples separately, again use the fpcf where needed. this time study both samples without pooling.. My preference would probably be the second. It is well known that these two groups are likely different and hence I would prefer to know about both of them. There is,of course, a third group of still nonrespondents, which are again different from the other two. You could try to sample those folks but diminishing returns starts to kick in. Always remember to use the fpcf where appropriate. If you have not already done your survey you could consider either a stratified (sometimes called a "representative" sample because various subpopulations are treated separately and thus are "representative" of their subgroups). Alternately a cluster approach could be adopted. All of these things used to be covered in a year long sequence of two courses often called Sampling I and I I. My favorite text was the following: https://www.amazon.com/Sampling-Techniques-3Rd-William-Cochran/dp/8126515244/ref=sr_1_1?keywords=William+G.+Cochran+Sampling+Technique&qid=1565833349&s=books&sr=1-1 Details on these things are all in this book. Sometimes people forget that the estimators are the same but the variances of the estimators are DIFFERENT than you see in the basic course. Most stat packages DON'T know this. However, some packages will charge you extra for a package that has the correct fpcf adjusted variances. DON'T FORGET TO USE THOSE. I loved these courses when I took them but then discovered the linear stat model and I had a new non-summer love. If you are a person that takes lots of samples like this then get a copy of Cochran's book. A summer love is better than no love at all. Best wishes, David Booth

James -

Your nonrespondents probably cannot be considered missing at random, so you do not have a probability-of-selection-based sample. You might try response propensity groups (you could research that) to try to approximate this, but with 40% nonresponse, that sounds iffy.

If you have regressor data on the whole population, you could try the model-based approach (see Royall below), where you are basically imputing for the missing data in such a way that you can get estimates of the variances of prediction errors. For applications of that done purposely for mostly small respondents, see Knaub presentation below.

The paper by Brewer below may be enlightening.

The two ways to deal with missing data in a sample are survey weight adjustment or imputation. For a census it is similar, as just described.

Cheers - Jim

"The model based (prediction) approach to finite population sampling theory," Institute of Mathematical Statistics Lecture Notes - Monograph Series, Volume 17, 1992, 225-240, Richard M. Royall,

 https://www.researchgate.net/publication/254206607_The_model_based_prediction_approach_to_finite_population_sampling_theory/, 

 https://projecteuclid.org/euclid.lnms/1215458849.    

"Quasi-Cutoff Sampling and the Classical Ratio Estimator - Application to Establishment Surveys for Official Statistics at the US Energy Information Administration - Historical Development," Knaub, 2017, invited presentation at US EIA, https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development

"Three controversies in the history of survey sampling," Survey Methodology, 12-001-X

Volume 39, Number 2

December 2013, Ken Brewer, KRW 

https://www150.statcan.gc.ca/n1/pub/12-001-x/2013002/article/11883-eng.htm

Once your sampling technique is census. Since you did not randomly sample there is an error