The desired precision of estimates, and therefore the necessary sample size, is a function of the planned use of the estimates. It is therefore impossible to make a general statement on how big a sample is necessary in each state. Instead, it is possible to look at a few illustrative characteristics for each subgroup and examine how often the precision will meet an arbitrary cut-off.
As mentioned earlier, the National Center for Health Statistics (NCHS) tries to ensure that all of its reported values that are analyzed in NCHS reports have a coefficient of variation (cv) less than or equal to 30 percent. Thus, for estimating fairly rare diseases with incidence rates of around 1.0 percent, this rule ensures that the standard error is no greater than 0.30 percentage points, yielding a 95 percent confidence interval of 1.0% ± 0.60%. For proportions closer to 50 percent this rule allows for much larger standard errors. A cv of 30 percent on such an estimate yields a 95 percent confidence interval of 50% ± 30%. Thus, depending on the size of the proportion estimated from the CPS and SIPP, it may be preferable to use different cut-offs for different characteristics.
Table 2 provided the estimated proportions for characteristics in question. The proportion receiving AFDC and the proportion with a work disability (except for the elderly) are both generally around 10 percent or less. For these two characteristics, we used the NCHS rule of a cv not greater than 30 percent. For the other two characteristics and disabled elderly, a smaller cv would be desirable. The estimates for poverty and employer-provided health insurance range from 11 to 60 percent. We chose an arbitrary confidence interval width of less than or equal to ±10 percent on these estimates.
As an alternative, all cut-offs could be specified in terms of standard errors, with larger standard errors acceptable for larger estimated percentages. For example, estimates under 10 percent could have a confidence interval width of ±2 percent, estimates of 20-40 percent a width of ±4 percent, and larger percents a width of ±5 percent. Another alternative for each population and characteristic would be to examine the distribution of standard errors achieved by the existing state samples.