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Accuracy, Bias, and Precision of Measurements

KEY WORDS accuracy, bias, collaborative trial, experimental error, interlaboratory comparison, preci-
sion, repeatability, reproducibility, ruggedness test, Youden pairs, Youden plots, Youden’s rank test.

In your otherwise beautiful poem, there is a verse which read,
Every moment dies a man, Every moment one is born.
It must be manifest that, were this true, the population of the
world would be at a standstill.…I suggest that in the next edi-
tion of your poem you have it read.
1
Every moment dies a man, Every moment 1------ is born.
16
…The actual figure is a decimal so long that I cannot get it into
the line, but I believe 1 16 is sufficiently accurate for poetry.
—Charles Babbage in a letter to Tennyson

The next measurement you make or the next measurement reported to you will be corrupted by
experimental error. That is a fact of life. Statistics helps to discover and quantify the magnitude of
experimental errors.
Experimental error is the deviation of observed values from the true value. It is the fluctuation or
discrepancy between repeated measurements on identical test specimens. Measurements on specimens
with true value η will not be identical although the people who collect, handle, and analyze the specimens
make conditions as nearly identical as possible. The observed values y i will differ from the true values
by an error ε i :
y i = η + ε i

The error can have systematic or random components, or both. If e i is purely random error and τ i is
systematic error, then ε i = e i + τ i and:
y i = η + ( e i + )
τ i
Systematic errors cause a consistent offset or bias from the true value. Measurements are consistently
high or low because of poor technique (instrument calibration), carelessness, or outright mistakes. Once
discovered, bias can be removed by calibration and careful checks on experimental technique and
equipment. Bias cannot be reduced by making more measurements or by averaging replicated measure-
ments. The magnitude of the bias cannot be estimated unless the true value is known.
Once bias has been eliminated, the observations are affected only by random errors and y i = η + e i .
The observed e i is the sum of all discrepancies that slip into the measurement process for the many steps
required to proceed from collecting the specimen to getting the lab work done. The collective e i may
be large or small. It may be dominated by one or two steps in the measurement process (drying, weighing,
or extraction, for example). Our salvation from these errors is their randomness.
The sign or the magnitude of the random error is not predictable from the error in another observation.
If the total random error, e i , is the sum of a variety of small errors, which is the usual case, then e i will
tend to be normally distributed. The average value of e i will be zero and the distribution of errors will
be equally positive and negative in sign.

© 2002 By CRC Press LLC