# The 2k Factorial Designs

The focus of this chapter is the development of special experimental designs involving factors having two levels each. The topics covered are:

• The factorial designs
• The 2k factorial designs
• Unreplicated 2k factorial designs
• Blocking the 2k factorial designs
• Confounding in the 2k factorial designs
• Yates’ algorithm for the 2k factorial designs
• The 2k fractional factorial designs
• One-half replication of a 2k factorial design
• One-quarter replication of a 2k factorial design

Learning Outcomes:

After studying this chapter, the reader will be able to

• Design and conduct special kinds of experiments in engineering or other scientific fields involving two or more factors.
• Create blocking appropriately to avoid any kind of confounding.
• Create blocking using appropriate interactions when experiments are designed using only one-half or one-quarter replication of a 2k design.
• Analyze data coming out of experiments employing some special techniques.
• Perform residual analysis to check the adequacy of the models under consideration.
• Summarize and interpret the results of these experiments.
• Use statistical packages MINITAB, Microsoft Excel, and JMP to analyze the data in these experiments.

## Introduction

We continue our discussion of factorial designs that began in Chapter 17. In this chapter we consider an important class of factorial designs in which each of the k factors has only two levels. Since these designs have exactly 2k treatments, they are usually ...

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