# Deriving State-Level Estimates from Three National Surveys: A Statistical Assessment and State Tabulations. D. Summary Results for the Selected Subgroups and Variables

The estimated proportions in Table 2 are very similar for both the CPS and SIPP. Therefore, the following analyses apply to both surveys. Poverty and health insurance both use the "confidence interval width of ±10 percent or less" rule and are therefore discussed before the two characteristics using the "cv of less than or equal to 30 percent" rule. Please note that the SIPP data combine information for nine states. Therefore, we assessed the 41 states and the District of Columbia for a total of 42 possible "states" from the SIPP.3

Poverty -- The minimum effective sample sizes necessary to achieve a 95 percent confidence interval width of ±10 percent or less for each sample proportion, p, can be calculated by solving the following formula for the effective sample size n. (where P is the population proportion with the characteristic):

To convert to the actual sample size, it is necessary to multiply n by the design effect shown in Table 3. For poverty this is 1.3. This leads to a minimum actual number of approximately 70 respondents for the total population, 110 for blacks or Hispanics, 95 children, and 55 elderly. The criteria differ slightly for the SIPP and the CPS. Both are presented in the appendices.

From the CPS, every state meets these minima for the total population, children, and the elderly (Table 5). Only 24 of the states have a sufficient sample for blacks and 19 states for Hispanics. From SIPP, every state assessed meets these minima only for the total population. The minima are also met for blacks in 20 states, Hispanics in 7 states, children in 35 states, and the elderly in 32 states.

Health Insurance -- The minimum actual sizes necessary to achieve a 95 percent confidence interval width of ±10 percent or less for the percentage receiving employer-provided health insurance is approximately 100 respondents for the total population and for each subpopulation. For the CPS, this is achieved for all states for the total population and children. The minimum is also met for blacks in 25 states, Hispanics in 20 states, and the elderly in 50 states. For the SIPP, this is achieved for all assessed states only for the total population. The minimum is also met for blacks in 20 states, Hispanics in 7 states, children in 34 states, and the elderly in 24 states.

AFDC -- The minimum effective sample size necessary to achieve a cv of less than or equal to 30 percent for each proportion, p, can be calculated by solving the following formula for n:

Note that on AFDC rates near 10 percent, this cv rule results in confidence intervals of ±6 percent. To convert to the actual sample size, it is necessary to multiply n by the design effect shown in Table 3. For AFDC this is 1.2. For the two surveys this leads to a minimum actual number of between 240 (for the SIPP) and 303 (for the CPS) respondents in a state for the total population and between 73 (for blacks from the SIPP) and 133 (for Hispanics from the CPS) for each of the subgroups. AFDC is generally not available to the elderly and therefore that subgroup is not considered for this characteristic.

From the CPS, every state meets these minima for the total population and children. Only 28 of the states have a sufficient sample for blacks and 16 states for Hispanics. From SIPP, the minima are met for the total population in 35 of the 42 assessed states, blacks in 20 states, Hispanics in 7 states, and children in 35 states.

Work Disability -- The minimum actual sizes necessary to achieve a cv of less than or equal to 30 percent for each proportion with a work disability ranges from 100 to 175 for all populations except the elderly and for children. Given that most children under 18 are not in the work force, their proportion with a work disability is also very small. Thus, while few states have the necessary completed interviews with more than 1,000 children, it is unlikely that such estimates will be necessary.

Given their relatively high frequency of disability, the necessary number of completes for the elderly is only 30. This number of completes is available from all states for the CPS and 24 states for SIPP. However, the resulting cv of 30 percent yields a confidence interval of 27% ± 16%. To achieve a confidence interval on this estimate that is no wider than ±10 percent would require 76 elderly respondents, a level reached in all CPS states other than Alaska, but only in 9 of the assessed SIPP states.

For the remaining populations, a cv of less than or equal to 30 percent requires from 100 to 175 completes. For the CPS, this is achieved for the total population in all states and for 27 states for blacks and 14 states for Hispanics. For the SIPP, a large enough number of completes for the total population is found in all of the assessed states except New Mexico and the District of Columbia, while it is only achieved for blacks in 20 states, and in 6 states for Hispanics.

It is worth noting that the work disability question on the CPS is being redesigned to correspond with the more extensive disability questions planned for the 2000 Census long form. Work disability will still be asked, but other types of disability will also be captured. Once wording for the new questions is finalized, they could be compared against other sources to predict the proportion with that type of disability and, by using the formulas in this section, to estimate the number of states that would support accurate estimates.

#### View full report

"deriving.pdf" (pdf, 2.83Mb)