Design of Experiments (DOE) versus Analysis of Variance (ANOVA)

QUESTION: If DOE essentially relies on multi-way Analysis of Variance (ANOVA) to arrive at the main effects, interaction, etc. why is it that we need fewer samples for conducting a DOE rather than doing a multi-way ANOVA?

RESPONSE: With a 2-level fractional factorial DOE, you can assess 15 factors 2-level in 16 trials, which is not unlike being able to conduct 15 t-tests where there is 8 trials at the high condition and 8 trials at the low condition in one experiment! This statement does not consider 2-factor interactions; however, there are some tricks of the trade to even discover potential two-factor interactions in such a resolution III experiment. You just don’t see ANOVA providing that amount of information for such few trials.

Consider also how both DOE and ANOVA provides probability values; however, DOE provides a direct estimate of the effect’s model, which often is very useful. For example, a DOE and ANOVA might indicate temperature and pressure are significant with p=0.02; however, the DOE directly provides an equation for expected response; e.g., Y=b + cTemp + dPressure.

This concept should be a part of Lean Six Sigma Black Belt training. DOE would fit into the improve phase of the project execution roadmap, shown at the bottom of Figure 2 in the article
“Corporate Performance Management: The Integrated Enterprise Excellence System.”