Example of Two-way ANOVA

An engineer wants to assess the relationship between sintering time and the compressive strength of three different metals. The engineer measures the compressive strength of five specimens of each metal type at each sintering time: 100 minutes, 150 minutes, and 200 minutes.

To test the statistical significance of the two factors, and the interaction between them, the engineer uses two-way ANOVA.

  1. Open the sample data, SinteringTime.MTW.
  2. Open the Two-way ANOVA dialog box.
    • Mac: Statistics > ANOVA > Two-Way ANOVA
    • PC: STATISTICS > ANOVA > Two-Way ANOVA
  3. In Response, enter Strength.
  4. In Factor 1, enter SinterTime.
  5. In Factor 2, enter MetalType.
  6. Select Include interaction term, then click OK.

Interpret the results

The p-values for the type of metal term and the interaction term are less than 0.05, which indicates that both terms have a statistically significant relationship with strength.

There is sufficient evidence to conclude that the type of metal is related to strength. The means table indicates that strength is highest (21.7778) with metal type 2.

However, the significant interaction indicates that the relationship between metal type and strength depends on the value of sinter time. Consequently, the engineer cannot interpret the main effects without considering the interaction effects.

If the engineer uses MetalType 2, SinterTime150 is associated with the highest mean strength (23.6667). However, if the engineer uses MetalType 1, SinterTime 100 is associated with the highest mean strength (21.3333).

To create a graph of the effects that are estimated by a two-way ANOVA model, use a factorial plot.

Factor Information
Factor
Levels
Values
100, 150, 200
1, 2, 3
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
SinterTime
MetalType
SinterTime*MetalType
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
Means
Term
Fitted Mean
SE Mean
100
150
200
1
2
3
100 1
100 2
100 3
150 1
150 2
150 3
200 1
200 2
200 3
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