APPENDIX B

Study Design and Reliability of the Estimates

Source of data. Estimates are based on data obtained from the 1977 Recipient Characteristics Study, which was designed to be representative of the March 1977 caseload. Data were provided by caseworkers assigned to the individual cases selected in the survey from case records on file. The caseworkers were provided uniform case schedules and instructions containing terminology designed to be comprehensible to all.

Sample design. Each State was required to draw a minimum sample of 1/3 of 1 percent or approximately 400 cases, whichever was larger, 1 from the universe of all families receiving an AFDC money payment during March 1977 (excluding partial payments). Cases consisting entirely of children receiving foster care were excluded from the study universe. The sample was designed to provide national estimates of 50 percent which would not vary from the true value being estimated by more than 1 percent, and State estimates of 50 percent which would not vary by more than 5 percent at the 95-percent confidence level. As shown in table B-1, some States (Alabama, Florida, Georgia, Maryland, Minnesota, Nebraska and North Carolina) sampled well above the minimum that was required.

Method of selection of sample. States were instructed to select sample cases based on a list of prescribed random digits associated with the case. All cases with numbers in the list of random numbers were to be included in the sample. For cases without an available social security number, another number containing randomly assigned digits, usually the case number, was to be used in the selection process.

Specifically, States were instructed to select their samples as follows: All AFDC cases with numbers that match the prescribed random numbers (N= count of prescribed random numbers) constitute the sample. For States with a caseload above 120,000 AFDC families, N = 34 4-digit random numbers.

For States with a caseload of 120,000 or fewer AFDC families, N = (Sample size/AFDC caseload) x 10,000. First, use the 34 4-digit random numbers. For the remaining (N-34) random numbers (table B-2):

For each additional 100 needed, select a 2-digit random number.

1There were 10 States or territories with caseloads of fewer than 10,000 cases for which the minimum required sample was less than 400, ranging from 334 for caseloads of 1,001-2,000 families to 385 for caseloads of 9,001 to 10,000 families.

Some States were unable to meet the prescribed method of sampling and instead submitted data based on a systematic design. Caseworkers were asked to complete schedules on their cases which had been selected in the sample.

After the exclusions from the March 1977 caseload, States submitted counts of the universe of families from which the samples were drawn. Each case was inflated by a weighting factor based on the universe used to sample. For example, the weighting factor for California was calculated as 298.96, i.e., 473,552 (the number of families in the universe) +1,584 (the number of case submitted in the sample). Integer value weights were assigned to facilitate data processing, n was the integer part of the calculated weight and n + 1 was assigned systematically to the fraction of cases represented by the decimal portion of the calculated weight. Thus, in the California example 4 percent of the cases were assigned 298 as a weight and 96 percent were assigned a weight of 299. National and regional estimates were derived from the summation of the inflated cases.

Reliability of the estimates. Because estimates contained in the report are based on a sample, data are subject to sampling variability, i.e., they may differ from results that would have been obtained from a complete enumeration of all cases. Particular care should be exercised in the interpretation of figures based on relatively small

numbers of cases as well as small differences between figures. As in any survey, the results are subject to errors of response and nonresponse and to sampling variability.

The schedule entries were based on current information in the case record, the worker's personal knowledge or the personal knowledge of another agency worker. However, information may not have been current, and other errors in reporting may have occurred due to misinterpretation or misunderstanding of the questions. There are no measures of the accuracy of the reported information in the current survey, but future studies will encompass an independent accuracy check based on a subsample of cases.

Nonresponse. States have reported instances where sample cases have been omitted because of discontinued payments and/or missing records. However, a comparison of the number of sample cases submitted with the number specified indicates that the number of such occurrences were negligible. The weighting factors were based on the number of sample cases actually submitted.

Sampling variability. As in all probability samples, such as the current study, the sampling variability can be measured. The standard error is the measure of that variability; that is of the variations that occur by chance because a sample rather than the entire population is surveyed. Standard errors for the estimates appearing in this report will be calculated precisely and made available upon request. The chances are about 68 in 100 that an estimate from the sample would differ from a complete Census figure by less than one standard error. The chances are about 95 in 100 that the difference would be less than 2 standard errors, and about 99 in 100 that the difference is less than 2.5 standard errors.