Chapter 11 ANOVA and Elements of Experimental Design
Design is art optimized to meet objectives.
– Shimon Shmueli
11.1 Introduction
In Chapter 10 we discussed the test of equality of means from two populations, H0: µ1 = µ2. Under standard assumptions of normality and independence, the proper test statistic followed a t-distribution, and several tests (equal/different variances, paired/unpaired samples) shared the common name “two-sample t-tests.”
Many experimental protocols involve more than two populations. For example, an experimenter may be interested in comparing the sizes of cells grown under several experimental conditions. At first glance, it seems that we can apply the t-test on all possible pairs of means. This “solution” would not be satisfactory since the probability of type I error for such a procedure is unduly large. For example, if the equality of four means is tested by testing the equality of 
= 6 different pairs, each at the level of 5%, then the ...
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