## About this lesson

## Exercise files

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ANOVA.xlsx10.8 KB ANOVA - Solution.docx

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## Quick reference

### ANOVA

ANOVA is a hypothesis test for comparing the means across multiple samples to determine if they are statistically equivalent.

### When to use

The ANOVA tool is widely used in Lean Six Sigma. It is the tool that is used in Gage R&R studies and with Design of Experiments. However, with respect to hypothesis testing, ANOVA is used to test for the equivalence of means across multiple samples when either the X or Y is discrete and the other is continuous.

### Instructions

ANOVA stands for ANalysis Of VAriance. It tests the means of multiple samples to determine their equivalence. Unfortunately, when the P Value is low and the Null hypothesis is rejected, the ANOVA does not specifically identify which sample was different. A further study of the data, or in the case of Minitab, the Boxplots, is needed to determine which sample is different.

The ANOVA function performs the same analysis as a Two-sample T Test. When there are only two samples, either hypothesis test can be used. However, when there are more than two samples, the ANOVA should be used. Multiple T Tests could be performed with every combination of samples, but each of those would be susceptible to a Type I Error. When doing multiple tests, the errors begin to compound.

Excel and Minitab can both calculate ANOVA for one or two Y variable. Minitab can also calculate an ANOVA with more than two variable.

- Excel – single Y variable
- Data Analysis > ANOVA Single Factor
- Enter data range, data must be in adjacent columns and each column is a sample set of data.

- Excel – two Y variables
- Data Analysis > ANOVA Two Factor without Replication
- Enter data range, data must be in adjacent columns and each column is a sample set of data

- Minitab – single Y variable
- Stat > ANOVA > One Way
- Select the format of your data and then the data columns
- With the Option button you can change the relationship and you can change the assumption of equal variances (based upon results of the Bartlett’s test).
- With the graphs button you can select the graph of your choice to visualize the comparison of the mean values.

- Minitab – multiple Y variables
- Stat > ANOVA > General Linear Model > Fit General Linear Model
- Select your Y Response variables
- Select you X Factor variables
- With the Model button, interaction between factors can be added as another variable.

### Hints & tips

- If your analysis indicates you should reject the Null hypothesis, rerun the analysis after dropping the data column that is the farthest from the other mean values.
- ANOVA is rather forgiving on the Normality assumption.

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