DOE Effects Analyzer

How do you analyze effects from a factorial experiment?

Effects analysis quantifies the impact of each factor and interaction on the response variable in a factorial experiment. A main effect is the change in the average response when a factor moves from its low (-1) to high (+1) level. An interaction effect occurs when the effect of one factor depends on the level of another.

The effect estimate for each term is calculated as the difference between the average response at the high level and the average response at the low level. ANOVA (Analysis of Variance) partitions the total variability into contributions from each factor and interaction, testing statistical significance via F-tests.

The Pareto chart of effects ranks all terms by absolute effect size, making it easy to identify the 'vital few' significant factors. R² indicates how much of the total variation is explained by the model. The percent contribution of each term shows its relative importance.

Formula: Effect = Ȳ(+1) - Ȳ(-1) SS_factor = (Effect)² × N / 4 F = MS_factor / MS_error R² = SS_model / SS_total % Contribution = SS_factor / SS_total × 100

Example Calculation

A 2² factorial with factors A and B. Responses: (−,−)=10, (+,−)=14, (−,+)=12, (+,+)=20. Effect A = ((14+20)/2) - ((10+12)/2) = 17 - 11 = 6. Effect B = ((12+20)/2) - ((10+14)/2) = 16 - 12 = 4. Interaction AB = ((10+20)/2) - ((14+12)/2) = 15 - 13 = 2. Factor A has the largest effect.

When to Use This Calculator

• After running a factorial experiment to determine which factors and interactions have statistically significant effects on the response
• During the Analyze phase of a Six Sigma DMAIC project to identify the vital few factors from a designed experiment
• When building a predictive model for process optimization — effect estimates and ANOVA provide the coefficients and significance levels for the model
• When deciding which factors to carry forward into a response surface study — only significant factors from the screening experiment should be included
• During experiment reporting to present a clear, quantified summary of factor contributions using Pareto charts and percent contribution tables

Common Mistakes to Avoid

• Ignoring interaction effects and only analyzing main effects — interactions can be as large or larger than main effects; always check at least 2-factor interactions
• Drawing conclusions from unreplicated experiments without understanding confounding — in unreplicated fractional factorials, effects are aliased; know your design's alias structure
• Over-interpreting percent contribution without statistical significance — a factor may show 15% contribution by chance; always check F-test p-values or use normal probability plots
• Including all possible interactions in the model regardless of significance — this overfits the model and consumes error degrees of freedom; use hierarchical modeling (include interactions only if the corresponding main effects are significant)

How to Interpret Results

• Start with the Effect Pareto Chart — terms with bars far taller than the rest are the vital few; a sharp drop-off after 2-3 terms is the typical 'sparsity of effects' pattern
• The sign of an effect Estimate tells the direction: a positive estimate means moving that factor from −1 to +1 increases the average response by that amount; a negative estimate decreases it
• % Contribution shows each term's share of total variation — terms contributing a few percent or less are usually noise even if they appear in the chart
• In the ANOVA table, a p-value below 0.05 marks a statistically significant term — but in saturated designs (no replicates with a full model) there are no residual degrees of freedom, so F and p cannot be computed; fall back on the Pareto chart and percent contribution
• Compare R² with adjusted R² — a large gap means the model carries insignificant terms; refit with fewer interaction orders and watch whether adjusted R² improves

Related Standards & References

• NIST/SEMATECH e-Handbook Chapter 5 — Process improvement through designed experiments, including effects analysis methodology
• ISO 3534-3 — Statistical vocabulary for design of experiments, defining effect, interaction, and confounding terms
• AIAG APQP 3rd Edition — Recommends DOE effects analysis for process parameter optimization during launch readiness

Frequently Asked Questions

How do I know if an effect is statistically significant?

With replicates, use ANOVA: if the F-statistic's p-value < α (typically 0.05), the effect is significant. Without replicates, use Lenth's method or a normal probability plot of effects — effects that deviate from the straight line are significant. The Pareto chart also helps by showing which effects are much larger than the rest.

What is the difference between main effects and interaction effects?

A main effect is the average change in response due to changing one factor, regardless of other factors' levels. An interaction effect means the impact of one factor depends on the level of another. For example, if temperature increases yield by 10% at low pressure but only 2% at high pressure, there is a temperature×pressure interaction. Ignoring interactions can lead to incorrect conclusions.