Omitting meaningless digits: Analyzing LDR(1), The standard leading-digit rule

Abstract

The standard leading-digit rule, LDR(1) is to omit point-estimator digits to the right of the leading digit of the point-estimator's standard error. Assuming that the original point estimator is normally distributed, the authors previously showed that LDR(1) guarantees-for all means and for all standard errors-that the truncated estimator's first omitted digit is correct with probability no greater than 0.117, not much greater than the 1-in-10 chance for a random digit. We consider two variations of the previously studied LDR(1) truncated point estimator, which in the worst case has non-negligible bias. The first is the truncated estimator with an implied appended digit ¿5¿. The second is the rounded estimator, which truncates after appending the ¿5¿. Both point estimators have nearly identical statistical properties, including negligible bias. Because of the omitted digits, however, the statistical quality of the two LDR(1) point estimators cannot be better than that of the original point estimator. In terms of root mean squared error and in terms of correlation with the original estimator, we establish here that the worst-case LDR(1) degradation is about four percent.