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

Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907
wheyming{at}ie.nthu.edu.tw
bruce{at}purdue.edu

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. Choosing the threshold to be about 0.198 yields Yoneda's rule. 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.

Subject classifications: statistical experiments; point estimator; standard error.
History: Received January 2006; revision received February 2007; accepted May 2007.