Choosing Between One‑Way ANOVA and Welch’s ANOVA in Minitab

Decision: Which ANOVA test should you run in Minitab?

When you need to compare the means of three or more independent groups, Minitab offers two primary options: the standard One‑Way ANOVA (which assumes equal variances) and Welch’s ANOVA (which relaxes that assumption). The choice hinges on whether the groups have similar variances and on the relative sizes of the samples. Selecting the wrong test can inflate Type I error or reduce power, leading to incorrect conclusions.

Constraints and assumptions

• Data must be continuous and approximately normally distributed within each group.
• Observations are independent.
• Sample sizes may be equal or unequal; both tests handle unequal n, but Welch’s is more robust when variances differ.
• Minitab version 19 or later provides both tests via the ANOVA menu (the same functionality exists from version 17 onward).

Comparison of supported options

Feature	One‑Way ANOVA	Welch’s ANOVA
Variance assumption	Equal variances required	No equal‑variance assumption
Sensitivity to unequal sample sizes	Moderate (can affect Type I error if variances differ)	Robust (maintains correct Type I error)
Power when variances are equal	Slightly higher	Slightly lower
Provides pooled variance estimate	Yes	No
Typical post‑hoc method	Tukey, Fisher LSD, etc.	Games‑Howell or Dunnett‑T3 (available in Minitab)
Menu path in Minitab	Stat > ANOVA > One‑Way…	Stat > ANOVA > Welch’s ANOVA…

Trade‑offs

If the equal‑variance assumption holds, One‑Way ANOVA gives you a modest power advantage and a pooled variance estimate that simplifies certain follow‑up analyses. However, when variances differ—especially with unequal group sizes—One‑Way ANOVA can produce an inflated false‑positive rate. Welch’s ANOVA protects the Type I error rate under heterogeneity at the cost of a small power loss and does not supply a pooled variance, which means you must use a post‑hoc procedure that does not rely on pooled variance (e.g., Games‑Howell).

Concrete implementation: Using Minitab’s Car sample data

This example shows how to run both tests and compare the results. No actual output is invented; the steps describe what you would see in the software.

1. Open Minitab and load the sample data set: Help > Sample Data, then select Car.MTW. The worksheet contains columns such as Price, MPG_City, and Origin (grouping variable with levels USA, Europe, Japan).
2. Prepare the data for a one‑way comparison of MPG_City across the three origins. Ensure the Origin column is set as a categorical variable (right‑click column > Format Column > Categorical).
3. Check variance equality (optional but recommended): Stat > ANOVA > Test for Equal Variances. Choose MPG_City as the response and Origin as the factor, then click OK. Note the p‑value; if it is below your alpha (e.g., 0.05), variances are likely unequal.
4. Run One‑Way ANOVA: Stat > ANOVA > One‑Way…. Set MPG_City as the Response and Origin as the Factor. Under Graphs, select Residual plots to examine normality. Click OK.
5. Run Welch’s ANOVA: Stat > ANOVA > Welch’s ANOVA…. Use the same Response and Factor selections. Again, you may request residual plots under Graphs. Click OK.
6. Compare the p‑values in the two session windows. If the equal‑variance test indicated heterogeneity, you will typically see a larger p‑value from Welch’s ANOVA (more conservative) and a smaller p‑value from One‑Way ANOVA (potentially anti‑conservative).
7. Examine the residual plots (normal probability plot and residuals versus fitted values) for each analysis to confirm the normality assumption is roughly satisfied. Severe deviations would suggest considering a non‑parametric alternative such as Kruskal‑Wallis.
8. If you proceed with Welch’s ANOVA and need pairwise comparisons, select Stat > ANOVA > Multiple Comparisons, choose the Welch’s ANOVA model, and pick Games‑Howell as the method.

Practical way to check the result

After each analysis, verify:

• The session window shows an ANOVA table with degrees of freedom, F‑value, and p‑value.
• Residual plots display no obvious patterns; points on the normal probability plot fall roughly along a straight line.
• If you used the equal‑variance test, its p‑value aligns with your decision (e.g., p < 0.05 → proceed with Welch’s).

These checks give you confidence that the chosen test matches the data’s characteristics.

Limitations

• Both ANOVA tests rely on approximate normality; with small sample sizes (< 10 per group) non‑normality can affect results more severely.
• Welch’s ANOVA does not produce a pooled variance, so certain effect‑size measures that depend on pooled variance (e.g., Cohen’s d based on pooled SD) must be computed manually or via alternative methods.
• Minitab’s Games‑Howell post‑hoc is available, but other heterogeneous‑variance procedures (e.g., Dunnett‑T3) may require additional steps or macros.

When assumptions are seriously violated, consider transforming the data or using a robust non‑parametric test.