A modified random groups standard error estimator

The standard error estimation method used for sample data in the U.S. Decennial Census from 1970 through 1990 yielded irregular results. For example, the method gave different standard error estimates for the "yes" and "no" response for the same binomial variable, when both standard error estimates should have been the same. If most respondents answered a binomial variable one way and a few answered the other way, the standard error estimate was much higher for the response with the most respondents. In addition, when 100 percent of respondents answered a question the same way, the standard error of this estimate was not zero, but was still quite high. Reporting average design effects which were weighted by the number of respondents that reported particular characteristics magnified the problem. An alternative to the random groups standard error estimate used in the U.S. census is suggested here.