Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 17

Analysis of Variance

The focus of this chapter is the development of various experimental designs involving one or more factors having fixed effects, random effects or mixed effects. The topics covered are:

• Design model and estimable functions
• One-way experimental layouts
• Multiple comparisons
• Determination of sample size
• The Kruskal–Wallis test for one-way layouts (Nonparametric Method)
• The randomized complete block design
• The Friedman F_r test for randomized complete block designs (RCB)
• Experiments with one missing observation in a RCB design experiment
• Experiments with several missing observation in a RCB design experiment
• Two-way experimental designs
• Two-way experimental layouts with one observation per cell
• Two-way experimental layouts with r (>1) observations per cell
• Blocking in two-way experimental designs
• Extending two-way experimental designs to n-way layout experimental designs
• Latin square designs
• The random effects model
• The mixed effects model
• Nested (hierarchical) design

Learning Outcomes:

After studying this chapter, the reader will be able to

• Design and conduct various kinds of experiments in engineering or other scientific fields involving one or more factors.
• Eliminate effects of one or more nuisance factors using appropriate experimental designs.
• Analyze data coming out of experiments with fixed, random, or mixed effects.
• Perform residual analysis to check the adequacy of the models under consideration.
• Use non-parametric techniques in certain kind ...