The main effects plot is most useful when you have several categorical variables. You can then compare the changes in the level means to see which categorical variable influences the response the most. A main effect is present when different levels of a categorical variable affect the response differently. For a variable with two levels, one level can increase the mean compared to the other level. This difference is a main effect. Main effects are only interpretable if the interaction effects are not significant.

Minitab creates the main effects plot by plotting the fitted mean for each value of a categorical variable. A line connects the points for each variable. Look at the line to determine whether or not a main effect is present for a categorical variable. Minitab also draws a reference line at the overall mean.

·    When the line is horizontal (parallel to the x-axis), then there is no main effect present. Each level of the variable affects the response in the same way, and the response mean is the same across all levels.

·    When the line is not horizontal (parallel to the x-axis), then there is a main effect present. Different levels of the categorical variable affect the response differently. The greater the difference in the vertical position of the plotted points (the more the line is not parallel to the X-axis), the greater the magnitude of the main effect.

By comparing the slopes of the lines, you can compare the relative magnitude of the effects.

Although a table of means and a plot of means provide the same numerical information, a plot can be easier to judge than a table of numbers. As always, plots indicate patterns. To determine if a pattern is statistically significant, check the p-value of the term in the analysis of variance table.

Factorial plots do not use the data in the worksheet. Instead, Minitab estimates the effects based on a stored model. You must fit a model with one or more categorical variables before you can generate a factorial plot. To produce an interaction plot, you must have two or more categorical variables. Factorial plots are accurate only if the model represents the true relationships.

For the plywood data, the plots indicate the following:

·    Diameter: Wider diameters are associated with higher torque than narrower diameters.

·    Penetrtn: Deeper penetration is associated with higher torque than shallower penetration.

·    Temp: Higher temperatures are associated with lower torque than lower temperatures.

The magnitude of the main effect for Diameter appears to be larger than the other variables. The main effects are only interpretable if the interaction effects are not significant.