Interpret the key results for Factorial Plots

Complete the following steps to interpret the factorial plots that illustrate a two-way ANOVA. Key output includes the interactions plot and the main effects plot.

Step 1: Show the interaction in the model

Use an interaction plot to show how the relationship between one categorical factor and a continuous response depends on the value of the second categorical factor. This plot displays means for the levels of one factor on the x-axis and a separate line for each level of another factor.

Evaluate the lines to understand how the interactions affect the relationship between the factors and the response.
Parallel lines
No interaction occurs.
Nonparallel lines
An interaction occurs. The more nonparallel the lines are, the greater the strength of the interaction.

Although you can use this plot to display the effects, be sure to perform the appropriate ANOVA test and evaluate the statistical significance of the effects. If the interaction effects are significant, you cannot interpret the main effects without considering the interaction effects.

In this interaction plot, the lines are not parallel. This interaction effect indicates that the relationship between metal type and strength depends on the value of sinter time. For example, if you use MetalType 2, SinterTime150 is associated with the highest mean strength. However, if you use MetalType 1, SinterTime 100 is associated with the highest mean strength.

The two-way ANOVA results indicate that the interaction between SinterTime and MetalType is significant.

Step 2: Show the main effects in the model

The main effects plot displays the means for each group within a categorical variable.

Minitab creates the main effects plot by plotting the means for each value of a categorical variable. A line connects the points for each variable. Look at the line to determine whether a main effect is present for a categorical variable. Minitab also draws a reference line at the overall mean. Interpret the line that connects the means as follows:
  • When the line is horizontal (parallel to the x-axis), there is no main effect present. The response mean is the same across all factor levels.
  • When the line is not horizontal, there is a main effect present. The response mean is not the same across all factor levels. The steeper the slope of the line, the greater the magnitude of the main effect.

Although you can use this plot to display the effects, be sure to perform the appropriate ANOVA test and evaluate the statistical significance of the effects. If the interaction effects are significant, you cannot interpret the main effects without considering the interaction effects.

In this main effects plot, it appears that SinterTime 150 is associated with the highest mean strength. However, the two-way ANOVA results indicate that this main effect is not statistically significant. The difference may be caused by random chance.

MetalType 2 is associated with the highest mean strength, and the two-way ANOVA results indicate that this main effect is significant.

The two-way ANOVA results indicate that the interaction between SinterTime and MetalType is significant. Consequently, you cannot interpret the main effects without considering the interaction effect.

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