One-way and two-way ANOVA

Learning objectives

• Distinguish one-way from two-way ANOVA.
• Interpret F, main effects and interaction.
• Follow up with planned comparisons.

What ANOVA does

One-way ANOVA compares means across one categorical factor. Two-way ANOVA adds a second factor and estimates their interaction.

A significant interaction means main-effect interpretation must be qualified — the effect of one factor depends on the level of the other.

Garment-factory example

Compare seam strength across four thread types; then analyse thread type and SPI together to see whether the thread effect changes with SPI.

Method

1. Define response and factors.
2. Randomise where possible.
3. Fit model in a free tool; inspect residuals.
4. Interpret interaction before main effects.

Common mistakes

• Running many pairwise t-tests instead of ANOVA.
• Interpreting main effects when a strong interaction exists.