Chapter 9: Q36E (page 552)
Define an experiment-wise error rate.
The risk of making a type I error applies to comparing the treatment means in the experiment. Thus, the value αselected is called an experiment-wise error rate.
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Forecasting electrical consumption. Two different methods of forecasting monthly electrical consumption were compared and the results published in Applied Mathematics and Computation (Vol. 186, 2007). The two methods were Artificial Neural Networks (ANN) and Time Series Regression (TSR). Forecasts were made using each method for each of 4 months. These forecasts were also compared with the actual monthly consumption values. A layout of the design is shown in the next table. The researchers want to compare the mean electrical consumption values of the ANN forecast, TSR forecast, and Actual consumption
a. Identify the experimental design employed in the study.
Identifying the type of experiment. Brief descriptions of a number of experiments are given next. Determine whether each is observational or designed and explain your reasoning.
a. An economist obtains the unemployment rate and gross state product for a sample of states over the past 10 years, with the objective of examining the relationship between the unemployment rate and the gross state product by census region.
b. A manager in a paper production facility installs one of three incentive programs in each of nine plants to determine the effect of each program on productivity.
c. A marketer of personal computers runs ads in each of four national publications for one quarter and keeps track of the number of sales that are attributable to each publication’s ad.
d. An electric utility engages a consultant to monitor the discharge from its smokestack on a monthly basis over a 1-year period to relate the level of sulfur dioxide in the discharge to the load on the facility’s generators.
e. Intrastate trucking rates are compared before and after governmental deregulation of prices changed, with the comparison also taking into account distance of haul, goods hauled, and the price of diesel fuel.
Robots trained to behave like ants. Robotic researchers investigated whether robots could be trained to behave like ants in an ant colony (Nature, August 2000). Robots were trained and randomly assigned to “colonies” (i.e., groups) consisting of 3, 6, 9, or 12 robots. The robots were assigned the task of foraging for “food” and to recruit another robot when they identified a resource-rich area. One goal of the experiment was to compare the mean energy expended (per robot) of the four different colony sizes.
a. What type of experimental design was employed?
Use Tables V, VI, VII, and VIII in Appendix D to find each
of the following F-values:
a. F0.05,v1=4,v2=4
b. F0.01,v1=4,v2=4
c. F0.10,v1=30,v2=40
d. F0.025,v1=15,v2=12
Evaluation of flexography printing plates. Refer to the Journal of Graphic Engineering and Design (Vol. 3, 2012) study of the quality of flexography printing, Exercise 9.24 (p. 544). Recall that four different exposure times were studied—8, 10, 12, and 14 minutes—and that the measure of print quality used was dot area (hundreds of dots per square millimeter). Tukey’s multiple comparisons procedure (at an experimentwise error rate of .05) was used to rank the mean dot areas of the four exposure times. The results are summarized below. Which exposure time yields the highest mean dot area? Lowest?
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