Omitting Meaningless Digits in Point Estimates: The Probability Guarantee of Leading-Digit Rules

Motivated by the question of which point-estimator digits to report in a statistical experiment, we study the probabilistic behavior of the digits as a function of the true performance measure and the point estimator's standard error. We investigate the family of Leading-Digit Rules, which guarantees that every unreported digit has correctness probability below a given threshold. We also propose a concise procedure and format for reporting a statistical point estimator and its precision in simulation experiments. Based on three criteria---minimal loss of statistical information, minimal number of digits required, and appeal to all levels of user sophistication---we claim that the leading-digit format provides an easy-read easy-print tabular report that is widely applicable and appealing to all levels of simulation users. The easy-to-implement rule that reports the point estimate through the leading digit of the standard error has threshold (approximately) $0.117$, which is not much larger than the one-in-ten probability of a uniformly distributed random digit being correct. Biography: Wheyming Tina Song is a Professor in the Department of Industrial Engineering at the National Tsing Hua University in Taiwan. She received her undergraduate degree in statistics and master's degree in industrial engineering at Cheng-Kung University in Taiwan in 1979. She then received master's degrees in applied mathematics in 1983 and industrial engineering in 1984, both from the University of Pittsburgh. She received her Ph.D. from the School of Industrial Engineering at Purdue University in 1989. She joined Tsing Hua in 1990 after spending one year as a visiting assistant professor at Purdue IE. Professor Song received the Outstanding University-Wide Teaching Award from the National Tsing Hua University in 1993. Her research honors include the 1988 Omega Rho (International Operations Research Honor Society) Outstanding Student Paper Award, the 1990 IIE Doctoral Dissertation Award, and the 1996 Distinguished Research Award from the National Science Council of the Republic of China. Information: email: [email protected] Fax: 6777-1434