# Multi-vari chart basics

## What is a multi-vari chart?

A multi-vari chart is a graphical representation of the relationships between factors and a response. Use a multi-vari chart to present analysis of variance data in a graphical form especially in the preliminary stages of data analysis to view data, possible relationships, and root causes for variation. Multi-vari charts are especially useful in understanding interactions.

Minitab draws multi-vari charts for up to eight factors. The chart displays the means at each factor level combination.

### Example of a four-factor multi-vari chart with mean connect lines for factor level means

In this example, Factor A and B have four levels each and Factor C and Factor D have two levels.

The chart that shows the average measurements separates the factor level combinations with vertical lines. Each cell displays the data points and the means for the factor level combinations. For example, the first cell shows the data points and the means for the factor level combination of A=1, B=1, C=1, D=1 and 2.

This multi-vari chart includes factor level mean lines for factors A, B, and C:
• A horizontal line that spans the first 8 cells shows the mean for factor A when A=1.
• A horizontal line that spans the first 2 cells shows the mean for factor B when B=1.
• A horizontal line that spans the first cell shows the mean for factor C when C=1.

The standard deviation chart shows the standard deviation for each factor level combination. The standard deviations in this example seem to vary relatively consistently.  ## What is an interaction?

Two factors interact if the effect of one factor on the response depends on the level of the other factor. An interaction between factors A and B would be denoted AB.

For example, suppose there are two routes you can drive home. One is the expressway and the other is a side road. Both routes have about the same distance, but the speed limit on the expressway is much higher. When traffic is light, the expressway takes much less time than the side road. But at rush hour, the traffic on the expressway slows so much that the side road is actually faster.

This is an example of an interaction between the two factors, route and time of day, where the response is the time home. In fact, this is the most extreme form of interaction, where the direction of an effect changes depending on the level of another factor. It would still be considered an interaction if the expressway was always the fastest route but the advantage was reduced at rush hour.

Non-rush hour Rush Hour
Expressway 30 minutes 1 hour
Side Road 45 minutes 45 minutes

You can also have three- and four-way interactions, which are more complicated to interpret.

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