The Test of Equal Variances conducts hypothesis tests for the equality variances using F, Bartlett's and Levene's tests. The F Test is performed in place of the Bartlett's test when there are only two levels.
Many statistical procedures like ANOVA and 2-Sample t-test assumes that samples are taken from populations with equal variances. This procedure can be used to valid this assumption.
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Null Hypothesis, H0 |
Alternate Hypothesis, H1 |
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s12 = s22 = . . . = si2 |
s12 ¹ s22 ¹ . . . ¹ si2 |
where si2 are the variances of population i.
1. Choose ProcessMA > ANOVA > Test of Equal Variances.
2. In Data in, choose how your data is stored.
· If your data in stored in a single column:
- In Variable, select the column containing the response
- In Category, select the column containing subgroup codes
· If your data in stored in different columns:
- In Variables, select the columns containing the separate responses.
3. Click OK.
Optional
4. In Test type, select the type of test(s) you want to run.
5. In Confidence level, enter the desired confidence level for the confidence interval.
6. Check Plot confidence interval, if you want to display the confidence intervals for the population standard deviation.
7. Check Plot boxplot, if you want to display the Boxplot of the data.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Variable: Numeric.
Category: Text or Numeric; Must have the same number of data points as the Variable; Must and contain at least 2 distinct categories.
Variables: Numeric.
Confidence level: Numeric; Between 0 and 100.
A company makes steel bolts using four different machines. You want to assess if the variation in dimensions of the steel bolts made are the same for the different machines. You randomly selected 50 steel bolts made by each machine.
1. Open worksheet ProcessMA > Tools > Data Files > Stat.xls.
2. Choose ProcessMA > ANOVA > Test of Equal Variances.
3. In Data in, select a single column.
4. In Variable, select N – Dimensions.
5. In Category, select O – Machine.
6. In Test type, select Both Tests.
7. In Confidence level, enter 95.
8. Check Plot confidence interval.
9. Check Plot boxplot.
10. Click OK.
Interpretation
The p-value of the tests is 0.3735 and 0.401 for Barlett’s and Levene’s tests respectively. For a desired a of 0.05, since p > a, we fail to reject H0. Therefore, we conclude that there is no significant evidence that the variances are different.