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Chapter 9: Q64E (page 579)

Suppose you conduct a 4 * 3 factorial experiment.

a. How many factors are used in the experiment?

b. Can you determine the factor type(s)—qualitative or quantitative—from the information given? Explain.

c. Can you determine the number of levels used for each factor? Explain.

d. Describe a treatment for this experiment and determine the number of treatments used.

e. What problem is caused by using a single replicate of this experiment? How is the problem solved?

Short Answer

Expert verified

e. The problem with this experiment's single replicate is the degrees of freedom for the error results in zero.

Step by step solution

01

Given Information

There are twelve treatment combinations used in the experiment.

02

Concept

The degrees of freedom for error with r replicate for a, and b factor levels are ab(r-1).

03

Determining the factor levels

e.

When a single replicate is used in the experiment, the error degrees of freedom become zero.

This problem is overcome by using the high order interaction pooling to estimate the error. Also, the normal probability plot for the error is used.

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Most popular questions from this chapter

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.

Mixed gender decision-making groups. In business, a group of executives is often assigned to make key decisions. The American Journal of Political Science (April 2014) published a study on a woman’s impact on mixed-gender deliberating groups. The researchers randomly assigned subjects to one of several 5-member decision-making groups. The

groups’ gender composition varied as follows: 0 females, 1 female, 2 females, 3 females, 4 females, or 5 females. Each group was then randomly assigned to utilize one of two types of decision rules: unanimous or majority rule. Ten groups were created for each of the 6 * 2 = 12 combinations of gender composition and decision rule. One variable

of interest, measured for each group, was the number of words spoken by women on a certain topic per 1,000 total words spoken during the deliberations.

a. Why is this experiment considered a designed study?

b. Identify the experimental unit and dependent variable in this study.

c. Identify the factors for this study. Give the levels of each factor.

d. How many treatments are in this study? List them.

Define an experiment-wise error rate.

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.

Corporate sustainability and firm characteristics. Refer to the Business and Society (March 2011) study on how firm size and firm type impact corporate sustainability behaviors, Exercise 1.28 (p. 51). Certified Public Accountants (CPAs) were surveyed on their firms’ likelihood of reporting sustainability policies (measured as a probability between 0 and 1). The CPAs were divided into four groups depending on firm size (large or small) and firm type (public or private): large/public, large/private, small/ public, and small/private. One goal of the analysis was to determine whether the mean likelihood of reporting sustainability policies differs depending on firm size and firm type. Identify each of the following elements for this study:

a. Experimental units

b. Response variable

c. Factor(s)

d. Factor levels

e. Treatments
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