Statistics for Environmental Engineers

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9

Accuracy, Bias, and Precision of Measurements


KEY WORDS accuracy, bias, collaborative trial, experimental error, interlaboratory comparison, precision, 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.


Every moment dies a man, Every moment 1 is born.


… 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 n will not be identical although the people who collect, handle, and analyze the specimens make conditions as nearly identical as possible. The observed values yt will differ from the true values by an error £■:


У, = n + £,


The error can have systematic or random components, or both. If et is purely random error and Tt is systematic error, then £; = et + т and:

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