27 - Analysis of Variance and Statistical Design of Experiments

Abstract

This chapter discusses the analysis of variance (ANOVA) and the statistical design of experiments. The experimental design determines the type of information that can be extracted from the data and therefore the type of ANOVA that must be used. While there are a number of specialized types of designs that have advantages in particular cases, most designs can be based on two types of “building blocks” for experimental designs. These building blocks depend upon whether the factors involved are controllable or not, and on whether or not they have systematic and reproducible effects. The terminology used to describe the experimental designs refers to whether factors are “crossed” or “nested” in the design. A table is presented with results obtained from the data previously used. The formalism of the ANOVA table specifies that the computations be performed in the order indicated. Since the ANOVA table is generated directly from the partitioning of the sums of squares, one column is called, appropriately enough “sums of squares,” and contains the corresponding sums of squares as entries. The statistic used for the test is the F statistic, which compares variances. Results show that the F found from the data is less than the critical F for these data.