# Example of Factorial Plots

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 show the results of the two-way ANOVA analysis, the engineer uses factorial plots.

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, and then click OK.
The model is now ready to use for factorial plots.
6. Open the Factorial Plots dialog box.
• Mac: Statistics > ANOVA > Factorial Plots
• PC: STATISTICS > Factorial Plots
7. In Response, select Strength, and then click OK.

## Interpret the results

The interaction plot shows the mean strength versus sintering time for each of the three metal types. This plot shows apparent interaction because the lines are not parallel, which implies that the relationship between sintering time and strength depends upon the type of metal. The output from the two-way ANOVA indicates whether the interaction is statistically significant.

When the lines on the interaction plot are not parallel, the means on the main effects plot can be misleading. Consequently, you cannot interpret the main effects without considering the interaction effects.

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

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