Creating and Analyzing a Two‑Level Factorial Design in Minitab

Quick answer

To create and analyze a two‑level factorial design in Minitab, use the Stat → DOE → Factorial → Create Factorial Design wizard to define factors and generate the run order, then run Stat → DOE → Factorial → Analyze Factorial Design on the collected data to obtain effect estimates, an ANOVA table and a Pareto chart.

Worked example: two factors, one replicate

1. Create the design

1. Open Minitab and choose Stat > DOE > Factorial > Create Factorial Design.
2. In the dialog, set Number of factors to 2.
3. Click Factors…, enter names (e.g., Temperature and Pressure) and set both as Numeric with low level –1 and high level +1.
4. Leave Number of replicates at 1 (you can add center points later if needed).
5. Keep Randomize runs checked to avoid systematic bias.
6. Click OK; Minitab fills the worksheet with columns for each factor, a RunOrder column, and a placeholder for the response.

2. Collect data and analyze

1. Enter your measured response values in the Response column corresponding to each run.
2. Choose Stat > DOE > Factorial > Analyze Factorial Design.
3. Select the response column, keep the default model (all main effects and interactions), and click OK.
4. Minitab outputs:
   • Effect estimates and coefficients.
   • ANOVA table showing p‑values for each term.
   • A Pareto chart of standardized effects (by default, effects with p < 0.05 appear in red).
   • Residual plots (normal probability plot, residuals vs. fitted) for assumption checks.

3. Verify the design

After creation, check that the run order follows a standard Yates order (for two factors: –1 –1, +1 –1, –1 +1, +1 +1) unless randomization changed it. You can sort the worksheet by RunOrder to confirm the pattern.

Limits and common mistakes

Limits

• Power: With only one replicate, the design can detect only relatively large effects. Minitab will show a power warning if the design is under‑powered, but it will not stop the analysis.
• Assumptions: The ANOVA assumes normality, independence and equal variance of residuals. Use the residual plots to verify; severe deviations may require transformation or a different design.
• Center points: Without center points you cannot detect curvature. Add them via Stat > DOE > Factorial > Create Factorial Design → Designs… → Center points if curvature is a concern.

Common mistakes

• Treating a numeric factor as categorical (or vice‑versa) changes the coding and leads to incorrect effect estimates. Always verify the factor type in the design table.
• Forgetting to randomize can introduce confounding with time‑related drift; keep the randomize option unless you have a specific reason to fix the order.
• Ignoring the residual diagnostics may cause you to trust a model that violates ANOVA assumptions, leading to misleading p‑values.

Practical way to check the result

After analyzing, look at the Normal Probability Plot of Residuals. If the points fall roughly along a straight line, the normality assumption is reasonable. Additionally, the Residuals vs. Fitted Values plot should show no obvious pattern; a funnel shape suggests non‑constant variance.