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References
Berthouex, P. M. and D. R. Gan (1991). “Fate of PCBs in Soil Treated with Contaminated Municipal Sludge,”
J. Envir. Engr. Div., ASCE, 116(1), 1–18.
Box, G. E. P. (1965). Experimental Strategy, Madison, WI, Department of Statistics, Wisconsin Tech. Report
#111, University of Wisconsin–Madison.
Box, G. E. P. (1966). “The Use and Abuse of Regression,” Technometrics, 8, 625–629.
Box, G. E. P. (1982). “Choice of Response Surface Design and Alphabetic Optimiality,” Utilitas Mathematica,
21B, 11–55.
Box, G. E. P. (1990). “Must We Randomize?,” Qual. Eng., 2, 497–502.
Box, G. E. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters: An Introduction to Design,
Data Analysis, and Model Building, New York, Wiley Interscience.
Colquhoun, D. (1971). Lectures in Biostatistics, Oxford, England, Clarendon Press.
Czitrom, Veronica (1999). “One-Factor-at-a Time Versus Designed Experiments,” Am. Stat., 53(2), 126–131.
Joiner, B. L. (1981). “Lurking Variables: Some Examples,” Am. Stat., 35, 227–233.
Pushkarev et al. (1983). Treatment of Oil-Containing Wastewater, New York, Allerton Press.
Tennessee Valley Authority (1962). The Prediction of Stream Reaeration Rates, Chattanooga, TN.
Tiao, George, S. Bisgarrd, W. J. Hill, D. Pena, and S. M. Stigler, Eds. (2000). Box on Quality and Discovery
with Design, Control, and Robustness, New York, John Wiley & Sons.

Exercises
22.1 Straight Line. You expect that the data from an experiment will describe a straight line. The

range of x is from 5 to 50. If your budget will allow 12 runs, how will you allocate the runs
over the range of x? In what order will you execute the runs?
22.2 OFAT. The instructions to high school science fair contestants states that experiments should
only vary one factor at a time. Write a letter to the contest officials explaining why this is
bad advice.
22.3 Planning. Select one of the following experimental problems and (a) list the experimental
factors, (b) list the responses, and (c) explain how you would arrange an experiment. Consider
this a brainstorming activity, which means there are no wrong answers. Note that in 3, 4, and
5 some experimental factors and responses have been suggested, but these should not limit
your investigation.

1. Set up a bicycle for long-distance riding.
2. Set up a bicycle for mountain biking.
3. Investigate how clarification of water by filtration will be affected by such factors as pH,
which will be controlled by addition of hydrated lime, and the rate of flow through the filter.
4. Investigate how the dewatering of paper mill sludge would be affected by such factors as
temperature, solids concentration, solids composition (fibrous vs. granular material), and
the addition of polymer.
5. Investigate how the rate of disappearance of oil from soil depends on such factors as soil
moisture, soil temperature, wind velocity, and land use (tilled for crops vs. pasture, for example).
6. Do this for an experiment that you have done, or one that you would like to do.

22.4 Soil Sampling. The budget of a project to explore the extent of soil contamination in a storage
area will cover the collection and analysis of 20 soil specimens, or the collection of 12
specimens with duplicate analyses of each, or the collection of 15 specimens with duplicate
analyses of 6 of these specimens selected at random. Discuss the merits of each plan.

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