Minitab®  Support

Manually calculate Bonferroni confidence intervals for the standard deviations (sigmas)

Learn more about Minitab

Complete the following steps to manually calculate the Bonferroni confidence intervals for the standard deviations (sigmas) of your factor levels instead of using Stat > ANOVA > Test for Equal Variances with the test based on the normal distribution.

Suppose you are using the Minitab sample data set HospitalComparison.MWX and analyzing the response Rating and factor Hospital, which has 2 levels. To calculate the confidence interval for Hospital A, using a familywise confidence level of 95% (0.95), do the following:

  1. Calculate K and store the value in a constant called K1.
    1. Open the Minitab sample data set HospitalComparison.MWX.
    2. Choose Calc > Calculator.
    3. In Store result in variable, enter K1.
    4. In Expression, enter 0.05 / (2 * 2).
    5. Click OK.
  2. Calculate the variance and sample size for each level of Method and store the results in the worksheet.
    1. Choose Stat > Basic Statistics > Display Descriptive Statistics.
    2. In Variables, enter Rating.
    3. In By variables (optional), enter Hospital.
    4. Click Statistics. Select Variance and N nonmissing.
    5. Click OK in each dialog box.
    For Hospital A, the variances is 66.9579 and the sample size is 20.
  3. Calculate U and store the result in worksheet constant named U1.
    1. Choose Calc > Probability Distributions > Chi-Square. For more information on the Chi-Square distribution, go to Chi-square distribution.
    2. Choose Inverse cumulative probability.
    3. In Degrees of freedom, type 19.
    4. Choose Input constant, and enter K1.
    5. In Optional storage, enter U1.
    6. Click OK.
  4. Calculate the upper bound for the confidence interval.
    1. Choose Calc > Calculator.
    2. In Store result in variable, enter UpperL1.
    3. In Expression, enter ((19 * 66.9579) / U1)**0.5.
    4. Click OK.
    The upper boundary for the 95% Bonferroni confidence interval for Hospital A is 12.6776. The lower bound is calculated the same way, using L instead of U.
  5. Calculate L and store the result in worksheet constant named L1.
    1. Choose Calc > Calculator.
    2. In Store result in variable, enter K3.
    3. In Expression, enter 1 - K1.
    4. Click OK.
    5. Choose Calc > Probability Distributions > Chi-Square.
    6. Choose Inverse cumulative probability.
    7. In Degrees of freedom, type 19.
    8. Choose Input column and enter K3.
    9. In Optional storage, enter L1.
    10. Click OK.
  6. Calculate the lower bound for the confidence interval.
    1. Choose Calc > Calculator.
    2. In Store result in variable, enter LowerL1.
    3. In Expression, enter ((19 * 66.9579) / L1)**0.5.
    4. Click OK.
    The lower bound for the 95% Bonferroni confidence interval for Hospital A is 5.99494.
    Note

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

Copyright © 2026 Minitab, LLC. All rights Reserved.