ROBUST DESIGN FOR SOFTWARE DEVELOPMENT - Software Design for Six-Sigma: A Roadmap for Excellence - page 495

TABLE 18.A.2 ANOVA Table

Source of VariationSum of SquaresDegree of Freedom Mean Squares F 0

SS A
a − 1

MS A
MS E

A SS A a − 1 MS A = F 0 =

SS B
b − 1

MS B
MS E

B SS B b − 1 MS B = F 0 =

SS AB
( a − 1)( b − 1) F 0 =

MS AB
MS E

AB SS AB (a − 1)(b − 1) MS AB =

Error SS E ab(n − 1)

Total SS T abn − 1

3. Compare the Fisher F test of the mean square of the experimental treatment
sources with the error to test the null hypothesis that the treatment means are
equal.
If the test results are in non-rejection region of the null hypothesis, then refine
the experiment by increasing the number of replicates, n , or by adding other
factors; otherwise, the response is unrelated to the two factors.
In the Fisher F test, the F 0 will be compared with the F-critical defin-
ing the null hypothesis rejection region values with appropriate degrees of
freedom; if F 0 is larger than the critical value, then the corresponding ef-
fect is statistically significant. Several statistical software packages, such
as MINITAB (Pensylvania State University, University Park, PA), can be
used to analyze DOE data conveniently, otherwise spreadsheet packages like
Excel (Microsoft, Redmond, WA) also can be used.
In ANOVA, a sum of squares is divided by its corresponding degree of
freedom to produce a statistic called the “mean square” that is used in the
Fisher F test to see whether the corresponding effect is statistically significant.
An ANOVA often is summarized in a table similar to Table 18.A.2.

Test for Main Effect of Factor A
Test statistic: F 0 , a − 1 , ab ( n − 1) =

MS A

MS E with a numerator degree of freedom equal
to ( a - 1) and denominator degree of freedom equal ab(n -1).
H 0 hypothesis rejection region: F 0 , a − 1 , ab ( n − 1) ≥

F α, a − 1 , ab ( n − 1) with a numer-

ator degree of freedom equal to ( a − 1) and denominator degree of freedom

equal to ab(n -1)

Test for Main Effect of Factor B
Test statistic: F 0 , b − 1 , ab ( n − 1) =

MS B

MS E with a numerator degree of freedom equal
to ( b - 1) and a denominator degree of freedom equal to ab(n -1).
H 0 hypothesis rejection region: F 0 , b − 1 , ab ( n − 1) ≥ F α, b − 1 , ab ( n − 1) with a numer-

−

ator degree of freedom equal to ( b 1) and a denominator degree of freedom

−

equal to ab(n 1)