The Problem of Nonresponse in Sample Surveys

The mail questionnaire is used in a number of surveys be cause of the economies involved. The principal objection to this method of collecting factual information is that it generally in volves a large nonresponse rate, and an unknown bias is involved in an assumption that responding are representative of the combined total of respondents and nonrespondents. Personal interviews generally elicit a substantially complete response, but the cost per schedule is, of course, considerably higher than it would be for the mail questionnaire method. The purpose of this paper is to indicate a technique which combines the advantages of both procedures. The problem considered is to determine the number of mail questionnaires to be sent out and the number of personal inter views to take in following up nonresponses to the mail ques tionnaire, in order to attain the required precision at a minimum cost. The procedure outlined below can be applied whatever the methods of collecting data are. For example, perhaps equally important as the problem of nonresponse in using mail question naires is the problem of call-backs in taking field interviews. In this latter problem the procedure to minimize cost for a given degree of reliability would call for taking a larger sample of first interviews and calling back on a fraction of those not at home. The technique presented herein makes it possible to use unbi ased designs at a reasonable cost where the excessive cost of ordinary methods of follow-up has frequently led to abandoning them. As an illustration, let us assume we want to estimate the num ber of employees in retail stores during a specified period in the State of Indiana. We shall assume we have a listing of all establishments having one or more employees, say from Social Security records, and their corresponding mailing addresses. A procedure sometimes followed is to take a sample of addresses from this list, mail out the questionnaires, and then depend ex clusively on the mail returns for the estimate of number of em ployees for all retail stores in the State. The result of this proce dure usually will be biased. It may be seriously so if there is a large rate of nonresponse. On the other hand, if all the addresses were actually visited by an enumerator, the cost of collecting the information would be much greater. Suppose the cost of mailing is 10 cents per questionnaire mailed, and the cost of processing the returns is 40 cents per questionnaire returned. Suppose, on the other hand, that the cost of carrying through field interviews is 4. 10 per questionnaire, and that this cost, together with the cost of processing the field returns, is 4. 50 per questionnaire. For the cost of one field visit we could then obtain about eight mail questionnaires with only a 20 percent response rate. This does not mean that we should take our entire sample by mail even though for the fixed cost we