Design and Sample Size Determination for Experiments on Nonresponse Followup using a Sequential Regression Model

Statistical agencies depend on responses to inquiries made to the public, and occasionally conduct experiments to improve contact procedures. Agencies may wish to assess whether there is significant change in response rates due to an operational refinement. This work considers the assessment of response rates when up to L attempts are made to contact each subject, and subjects receive one of J possible variations of the operation under experimentation. In particular, the continuation-ratio logit (CRL) model facilitates inference on the probability of success at each step of the sequence, given that failures occurred at previous attempts. The CRL model is investigated as a basis for sample size determination– one of the major decisions faced by an experimenter–to attain a desired power under a Wald test of a general linear hypothesis. An experiment that was conducted for nonresponse followup in the United States 2020 decennial census provides a motivating illustration.