Terminal digits and the examination of questioned data

Accountability in Research

Volumn 9, Issue 2, 2002, Pages 75-92

  Mosimann, James E ^a   Dahlberg, John E ^b   Davidian, Nancy M ^b   Krueger, John W ^b  

^a ABL Associates Inc   (United States)

^b U S DEPARTMENT OF HEALTH AND HUMAN SERVICES   (United States)

Author keywords

Scientific misconduct; Statistical forensics; Terminal digits; Uniform digits

Indexed keywords

EID: 10944262422     PISSN: 08989621     EISSN: 15455815     Source Type: Journal    
DOI: 10.1080/08989620212969     Document Type: Article

References (12)

1. 65 Federal Register 76260, December 6, 2000.
2. A theoretical discussion is found in J. E. Mosimann and M. V. Ratnaparkhi, "Uniform occurrence of digits for folded and mixture distributions on finite intervals, " Communications in Statistics, 1996, 25(2), pp. 481-506. Among other issues, this paper discusses approximations to continuous distributions by histogram distributions for which the uniformity of terminal digits up to a specified place is known. Such theoretical issues are important, but our emphasis here is on direct comparison of questioned data with unquestioned data.
3. On May 1, 1995, the Maryland Lottery initiated a midday pick-3 drawing for weekdays. This is in addition to the nightly drawing. Thus, there are more than 3,650 winning pick-3 numbers over the ten-year period. Maryland Lottery results may be found at the official Web site, http://www.mdlottery.com.
4. In all there are 474 counts: 252 admittedly falsified (notebook pages; 141-152); and 222 unquestioned counts that are supported by counter printouts (notebook pages; 104-106,130-131, 134-135). Each count, falsified or unquestioned, contains from three to six digits. Digits were tested in four places, but no digit that was itself the leftmost digit was included in the analysis. Total analyses included 939 digits from 252 falsified numbers and 857 digits from 222 unquestioned numbers.
5. See "Data fabrication: Can people generate random digits?" J. E. Mosimann, C. V. Wiseman, and R. E. Edelman, Accountability in Research, 4, 31-55, 1995. This study shows that many people have difficulty fabricating random digits, even when trying to do so.
6. "Inverse" sampling until a certain number of a particular event occurs has a long history, particularly where rare events are to be studied. (For example, see J. E. Mosimann, "On the compound negative multinomial distribution and correlations among inversely sampled pollen counts, " 1963, Biometrika, 50, 47-54).
7. "It is conventional to round off to the nearest even digit when the number to be rounded is exactly half way between two successive digits. " pp. 13-14, Paul S. Dwyer, Linear Computations, 1951, John Wiley & Sons, Inc. (See also the next two footnotes.)
8. "PowerBASIC always rounds towards the closest even number. For example, both 1.5 and 2.5 would be rounded to 2. This is called banker's rounding. " p. 169, User's Guide, 1997, PowerBASIC, Inc. 316 Mid Valley Center, Carmel, California, i-vi, 1-318.
9. ANSI/IEEE Std 854-1987, October 5, 1987, "ANSI" denotes the American National Standards Institute and "IEEE" denotes the Institute of Electrical and Electronic Engineers, Inc. "4.1 Round to Nearest. if the two nearest representable values are equally near, the one with its least significant digit even shall be delivered. " "5.4 Round Floating Point Number to Integral Value. when rounding to nearest, if the difference between the unrounded operand and the rounded result is exactly one half, the rounded result is even. "
10. 46 of these 58 time values that terminate in odd digits occur with amplitudes greater than 20 picoAmps. In the initial 321 records of Experiment 1, 6 of 6 odd time values occur with amplitudes greater than 20 picoAmps.
11. It is only after the respondent denied the charges and findings of the institution that the ORI demonstrated which two rats on the spreadsheet represented falsified data, and the manner of falsification.
12. The spreadsheet also contains columns of numbers representing blood pressure measurements and radioactive counts, some of which the university committee regarded as falsified. These are not presented here.