Abstract The mail questionnaire is used in a number of surveys because of the economies involved. The principal objection to this method of collecting factual information is that it generally involves a large non-response rate, and an unknown bias is involved in any assumption that those responding are representative of the combined total of respondents and non-respondents. 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 principle followed is to mail schedules in excess of the number expected to be returned, and to follow up by enumerating a sample of those that do not respond to the mail canvass. Under reasonable assumptions as to the relative costs of the two methods of canvass, an allocation of the sample can be made to mail and field canvasses. An illustration is given to show for a given degree of reliability, the varying sizes of the mailing list for different expected response rates, and the rate of field follow-up on the non-responses. For each response rate, the minimum cost of the survey is computed; from this computation it is possible to determine the maximum number of schedules to be mailed independent of the rate of response. Then to achieve the desired precision, the number to be interviewed would vary with the response rate actually found. In a mathematical appendix the general formulas are derived.
Hansen et al. (Sun,) studied this question.