### What is Multi Vari Analysis?

Multi Vari analysis is a graphic-driven method to analyze the effects of categorical inputs on a continuous output. It studies how the variation in the output changes across different inputs and helps us quantitatively determine the major source of variability in the output. Multi-Vari charts are used to visualize the source of variation. They work for both crossed and nested hierarchies.

- Y: continuous variable
- X’s: discrete categorical variables. One X may have multiple levels

### Hierarchy

Hierarchy is a structure of objects in which the relationship of objects can be expressed similar to an organization tree. Each object in the hierarchy is described as above, below, or at the same level as another one. If object A is above object B and they are directly connected to each other in the hierarchy tree, A is B’s parent and B is A’s child. In Multi-Vari analysis, we use the hierarchy to present the relationship between categorical factors (inputs). Each object in the hierarchy tree indicates a specific level of a factor (input). There are generally two types of hierarchies: crossed and nested.

**Crossed Hierarchy**– In the hierarchy tree, if one child item has more than one parent item at the higher level, it is a crossed relationship.**Nested Hierarchy –**In the hierarchy tree, if one child item only has one parent item at the higher level, it is a nested relationship.

### Use Minitab to Perform Multi Vari Analysis

Case study: ABC Company produces 10 kinds of units with different weights. Operators measure the weights of the units before sending them out to customers. Multiple factors could have an impact on the weight measurements. The ABC Company wants to have a better understanding of the main source of variability existing in the weight measurement. The ABC Company randomly selects three operators (Joe, John, and Jack) each of whom measures the weights of 10 different units. For each unit, there are three items sampled.

Data File: “Multi-Vari” tab in “Sample Data.xlsx.”

Steps in Minitab to perform a Multi-Vari Analysis:

- Click Stat → Quality Tools → Multi-Vari Chart.
- A window named “Multi-Vari Chart” pops up.
- Select “Measurement” as the “Response,” “Unit” as “Factor 1,” and “Operator” as “Factor 2.”

- Click “Options” button.
- A new window named “Multi-Vari Chart” appears.
- Check the box of “Display individual data points.”

- Click “OK.”
- Analyze the Multi-Vari chart to determine the major source of the variation in the output.

#### Interpreting Minitab’s Multi-Vari Analysis

Model summary: Based on the Multi-Vari chart ouptu, the measurement of units ranges from 0.4 to 1.1. Joe’s and John’s mean measurements stay between 0.8 and 0.9. Jack’s mean is slightly lower than both Joe’s and John’s. John has the worst variation when measuring the same kind of unit because John has the highest difference between the maximum and minimum bars for any kind of unit. By observing the black lines of three operators, it seems like all three operators’ measurements follow the same pattern. The operator-to-operator variability is not large. The unit-to-unit variability is large and it could be the main source of variation in measurements.

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