Analysis of Variance & Design of Experiments

In statistical inference we have seen the test of significance of the difference of two means
i.e., whether two samples differ significantly with respect to some property or not. In
actual practice, however, it often happens that more than two samples are involved in a
study. For example in an agricultural experiment, four different chemical treatments of
soil say A B C and D produce mean wheat yields of 28, 22, 18 and 24 bushels per acre
respectively. If we want to test whether there is a significant difference in these means or
it is due to chance only then we cannot use t-test for equality of these means.

However, one way of using t-test is that we make pairs of two treatments and then test them, i.e., we
test AB AC AD BC BD CD separately, and conclusion is also drawn separately for
each pair. In other words ' 't test will be applied 6 times and still a joint significance test
will not be available. Thus ' 't test is not suitable in this case because we want a test which
provides inference for all the 4 treatments for separately for pairs. Such problems can be
solved by using an important technique known as "Analysis of Variance" developed by
Prof. R.A. Fisher in 1923. It makes use of F-distribution.

Chapter 1: Analysis of Variance
Chapter 2: Design of Experiments
Chapter 3: Factorial Experiments