Add-a-Digit Sampling

Add-a-digit sampling is a method of creating a sample of telephone numbers to reach the general public within some geopolitical area of interest. This method is related to directory sampling in that the first step involves drawing a random sample of residential directory-listed telephone numbers from a telephone directory that covers the geographic area of interest. In add-a-digit sampling, the selected directory-listed telephone numbers are not called. Rather, they form the seeds for the list of numbers that will be called. For each directory-listed telephone number drawn from the telephone directory, the last digit of the telephone number is modified by adding one to the last digit. The resulting number is treated as one of the telephone numbers to be sampled. This is the simplest form of add-a-digit sampling. When it was originally devised in the 1970s, it was an important advancement over directory-listed sampling in that the resulting sample of telephone numbers included not only listed numbers but also some numbers that were unlisted residential telephone numbers.

Another practice is to take a seed number and generate several sample telephone numbers by adding 1, 2, 3, 4, 5, and so on to the last digit of the telephone number. However, in the application of this technique, it was found that the higher the value of the digit added to the last digit of the seed telephone number, the less likely the resulting telephone number would be a residential number. Still another method involves drawing the seed telephone numbers and replacing the last two digits with a two-digit random number.

Add-a-digit sampling originated as a method for including residential telephone numbers that are not listed in the telephone directory in the sample. These unlisted numbers are given a zero probability of selection in a directory-listed sample. In add-a-digit sampling, some unlisted telephone numbers will be included in the sample, but it is generally not possible to establish that all unlisted residential telephone numbers have a nonzero probability of selection. Moreover, it is difficult to determine the selection probability of each telephone number in the population, because the listed and unlisted telephone numbers may exhibit different distributions in the population of telephone numbers. For example, one might encounter 500 consecutive telephone numbers that are all unlisted numbers. Because of these and other limitations, add-a-digit [Page 7]sampling is rarely used today. It has been replaced by list-assisted random-digit dialing.