ROBUST DESIGN FOR SOFTWARE DEVELOPMENT - Software Design for Six-Sigma: A Roadmap for Excellence - page 492

analysis of variance extends the two-sample t test for testing the equality of two
population means to a more general null hypothesis of comparing the equality of more
than two means versus them not all being equal. ANOVA includes procedures for
fitting ANOVA models to data collected from several different designs and graphical
analysis for testing equal variances assumption, for confidence interval plots as well
as graphs of main effects and interactions.
For a set of experimental data, most likely the data varies as a result of chang-
ing experimental factors, whereas some variation might be caused by unknown or
unaccounted for factors, experimental measurement errors, or variation within the
controlled factors themselves.
Several assumptions need to be satisfied for ANOVA to be credible, which are as
follows:

1. The probability distributions of the response ( y ) for each factor-level combina-
tion (treatment) is normal.
2. The response ( y ) variance is constant for all treatments.
3. The samples of experimental units selected for the treatments must be random
and independent.

The ANOVA method produces the following:

1. A decomposition of the total variation of the experimental data to its possible
sources (the main effect, interaction, or experimental error);
2. A quantification of the variation caused by each source;
3. Calculation of significance (i.e., which main effects and interactions have sig-
nificant effects on response ( y ) data variation).
4. Transfer function when the factors are continuous variables (noncategorical in
nature).

18.A.1 ANOVA STEPS FOR TWO FACTORS COMPLETELY
RANDOMIZED EXPERIMENT 17

1. Decompose the total variation in the DOE response ( y ) data to its sources (treat-
ment sources: factor A; factor B; factor A factor B interaction, and error).

The first step of ANOVA is the “sum of squares” calculation that produces the
variation decomposition. The following mathematical equations are needed:

×

j = 1

b

k = 1

n

y ijk

y i .. = (Row average) (18.A.1)

bn

17 See Yang and El-Haik (2008).