About this lesson
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.
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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