Complete the following steps to manually calculate the Bonferroni confidence intervals for the standard deviations (sigmas) of your factor levels instead of using .

orSuppose you are using the Minitab sample data set CarLockRatings.MTW and analyzing the response Usability Rating and factor Method, which has 2 levels. To calculate the confidence interval for Method 1, using a familywise confidence level of 95% (0.95), do the following:

- Calculate K and store the value in a constant called K1.
- Open the Minitab sample data set CarLockRatings.MTW.
- Choose .
- In Store result in variable, enter
`K1`. - In Expression, enter
`0.05 / (2 * 2)`. - Click OK.

- Calculate the variance and sample size for each level of Method and store the results in the data window.
- Choose .
- In Variables, enter Usability Rating.
- In By variables (optional), enter Method.
- Click Statistics. Select Variance and N nonmissing.
- Click OK in each dialog box.

For Method 1, the variances is 1.02841 and the sample size is 33. - Calculate U and store the result in worksheet constant named U1.
- Choose .
- Choose Inverse cumulative probability.
- In Degrees of freedom, type
`32`. - Choose Input column, and enter
`K1`. - In Optional storage, enter
`U1`. - Click OK.

- Calculate the upper bound for the confidence interval.
- Choose .
- In Store result in variable, enter
`UpperL1`. - In Expression, enter
`((32 * 1.02841) / U1)**0.5`. - Click OK.

The upper boundary for the 95% Bonferroni confidence interval for Method 1 is 1.39977. The lower bound is calculated the same way, using L instead of U. - Calculate L and store the result in worksheet constant named L1.
- Choose .
- In Store result in variable, enter
`K2`. - In Expression, enter
`1 - K1`. - Click OK.
- Choose .
- Choose Inverse cumulative probability.
- In Degrees of freedom, type
`32`. - Choose Input column and enter
`K2`. - In Optional storage, enter
`L1`. - Click OK.

- Calculate the lower bound for the confidence interval.
- Choose .
- In Store result in variable, enter
`LowerL1`. - In Expression, enter
`((32 * 1.02841) / L1)**0.5`. - Click OK.

The lower bound for the 95% Bonferroni confidence interval for Method 1 is 0.791436.###### Note

When there is more than one factor, you need to consider each distinct factor level combination as a separate factor level.