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Handling Misconduct - Technical Assistance
Statistical Forensics: One Digit Too Many!
When the original handwritten data contain only three
decimal places, and the same data entered into a Microsoft Excel7
spreadsheet appear with four decimal places, there is cause
for suspicion. Where did that extra digit come from? And when that
fourth digit is either a zero or a five, (and no other
digit, e.g., one or nine) the suspicion is that division
by two produced the fourth decimal digit. Thus, division
by two of a decimal number whose last digit is odd
leaves a remainder of one-half which produces an extra decimal
digit, five. In contrast, when the last digit is even, there
is no remainder and the extra digit is zero. Division by
two yields no other extra digits.
In one case, these clues led investigators of ORI's
Division of Investigative Oversight (DIO) to determine that the
data for a third rat were fabricated by averaging the data for two
others. This case concerned a study of the effect of rhythmic contractions
of skeletal muscle in the hind limbs of rats where blood flow was
measured at rest and during nerve stimulation. Measurements of blood
flow and muscle weight were recorded.
The respondent presented results for six rats in a
lab seminar. Sometime after that, a co-worker discovered that the
original data sheets for two rats were blank. The respondent furnished
the university with copies of tracings of continuous measurements,
handwritten recorded data for muscles for six rats, and printouts
of a Microsoft Excel7
spreadsheet that contained blood pressure measurements and muscle
weights for six rats.
DIO investigators concentrated on the measurements
of muscle weight. The investigators observed that the entries in
the spreadsheet for Rat-3 and Rat-6, purportedly copied from the
handwritten data sheets, had an extra decimal digit. Therefore,
the spreadsheet numbers had not been copied from the handwritten
sheets. They further observed that the extra digit was either five
or zero. This observation led to the hypothesis that the
Rat-3 and Rat-6 measurements were the average of two measurements.
Investigators then verified that the purported measurements for
"Rat-3" and "Rat-6" were the averages of the
corresponding measurements, respectively, for Rat-1 with Rat-2,
and Rat-4 with Rat-5. This irrefutable demonstration that the weights
for both Rat-3 and Rat-6 were fabricated by calculation facilitated
the voluntary exclusion of the respondent from receiving Federal
funds for 3 years.
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