ANOVA Statistics (Response to Question from k.dhiyanes )

[Ranjit Roy]

Hello k.dhiyanes,

1.ANOVA is like the chest X-ray of a person. It is what it is. As long
as the calculations are correct, all we need to do is to understand
and interpret it well. The relative values of the factors and
interactions ANOVA shows should be accepted as they are. Thus in your
system, the fact is that influence of factors E & D are higher, the
remaining factors and interactions happen to have small amount of
influence.

The error effect (1.43%) is a good thing and credits your experiment
planning effort as it primarily reflects that the factors you included
in the study were indeed the influencing sources.

When interaction is significant, it will, of course, have influence on
the “performance/result”. What it means is that the prediction you are
able to make from the DOE results may not come closer to actual
performance (Confirmation Tests Results) unless you make CORRECTIONS
for interaction effects. Making corrections for significant
interaction is slightly complicated, but commonly done. Such
corrections for interactions make the prediction of performance come
closer to actual performance thereby validating the analysis. This
process can be quite difficult when interactions are too many as they
may suggest conflicting corrections (suggesting different levels of
the same factor).

Quite often, however, small interaction effects are ignored with the
hope that design recommendations without interactions show good
CONFIRMATION. If the results confirms prediction from analysis, that
means that the interactions, even if present, have minimum influence
on the result.

In your case, the following approach may work:
(a) Ignore interaction (AxB =2.14 %, AxC =1.43% and BxC
=1.43% ) and proceed to run confirmation tests with optimum condition
without interaction. If you confirm, you should be satisfied.
(b) If you do not confirm, you may then proceed to make
corrections for interaction and re-determine OPTIMUM DESIGN and
estimate of performance. You will give yourself a better chance to
confirm this time. If you do not confirm here, the noise effects
dominate and you should go for ROBUST DESIGN.

It is difficult for me to comment of your “linear equation” without
more information. Just be aware that the expression for “Yopt = “ (in
QUalitek-4 or Nutek literature) represents a linear equation that
includes influences of factor and is a predictor of performance not
only at the optimum condition, but for all possible full-factorial
combinations.

Good luck.

- Ranjit Roy 2/10/2011