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and minuses indicate the two levels of each factor to be investigated. Notice that each factor is studied
four times at a high (+) level and four times at a low (−) level. There is a desirable and unusual balance
across all k = 7 factors. These designs exist for N = k + 1, as long as N is a multiple of four. The analysis
of these factorial designs is explained in Chapters 27 to 30.

Comments
An accurate measurement has no bias and high precision. Bias is systematic error that can only be removed
by improving the measurement method. It cannot be averaged away by statistical manipulations. It can
be assessed only when the true value of the measured quantity is known.
Precision refers to the magnitude of unavoidable random errors. Careful measurement work will
minimize, but not eliminate, random error. Small random errors from different sources combine to make
larger random errors in the final result. The standard deviation (s) is an index of precision (or imprecision).
Large s indicates imprecise measurements. The effect of random errors can be reduced by averaging
replicated measurements. Replicate measures provide the means to quantify the measurement errors and
evaluate their importance.
Collaborative trials are used to check for and enforce consistent quality across laboratories. The Youden
pairs plot is an excellent graphical way to report a laboratory’s performance. This provides more information
than reports of averages, standard deviations, and other statistics.
A ruggedness test is used to consider the effect of environmental factors on a test method. Systematic
changes are made in variables associated with the test method and the associated changes in the test
response are observed. The ruggedness test is done in a single laboratory so the effects are easier to see,
and should precede the interlaboratory round-robin study.

References
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Clesceri, L. S., A. E. Greenberg, and A. D. Eaton, Eds.
ASTM (1990). Standard Guide for Conducting Ruggedness Tests, E 1169-89, Washington, D.C., U.S. Gov-
ernment Printing Office.
ASTM (1992). Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a
Test Method, E691-92, Washington, D.C., U.S. Government Printing Office.
ASTM (1993). Standard Practice for Generation of Environmental Data Related to Waste Management
Activities: Quality Assurance and Quality Control Planning and Implementation, D 5283, Washington,
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Maddelone, R. F., J. K. Rice, B. C. Edmondson, B. R. Nott, and J. W. Scott (1993). “Defining Detection and
Quantitation Levels,” Water Env. & Tech., Jan., 41–44.
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