TABLE OF CONTENTS This chapter begins our consideration of single-factor experiments. To ensure that a given design will be completely randomized, Chapter 3 places no restrictions on the randomization. Many of the techniques of analysis for a completely randomized single-factor experiment can be applied with little alteration to more complex experiments.
For example, the single factor could be steel manufacturers, where the main interest of an analyst centers on the effect of several different manufacturers on the hardness of steel purchased from these vendors. It could be temperature, if the experimenter is concerned about the effect of this variable on pemci1lm Yield. In cases such as these, where only one factor is varied, the experiment is referred to as a single-factor experiment. The symbol ? j will be used to indicate the effect of the jth level of the factor, suggesting that the general factor may be thought of as a "treatment" effect.
If the order of experimentation applied to the several levels of the factor is completely random, so that any material to which the treatments might be applied is considered to be approximately homogeneous, the design is called a completely randomized design. The number of observations for each level of the factor will be determined from cost considerations and the power of the test. The model then becomes
with Y ij the ith observation ( i = 1, 2, , n j) on the j
