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

Complete the following steps to manually calculate the Bonferroni confidence intervals for the standard deviations (sigmas) of your factor levels instead of using Stat > Basic Statistics > 2 Variances or Stat > ANOVA > Test for Equal Variances.

Suppose 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:

  1. Calculate K and store the value in a constant called K1.
    1. Open the Minitab sample data set CarLockRatings.MTW.
    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 data window.
    1. Choose Stat > Basic Statistics > Store Descriptive Statistics.
    2. In Variables, enter Usability Rating.
    3. In By variables (optional), enter Method.
    4. Click Statistics. Select Variance and N nonmissing.
    5. Click OK in each dialog box.
    For Method 1, the variances is 1.02841 and the sample size is 33.
  3. Calculate U and store the result in worksheet constant named U1.
    1. Choose Calc > Probability Distributions > Chi-Square.
    2. Choose Inverse cumulative probability.
    3. In Degrees of freedom, type 32.
    4. Choose Input column, 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 ((32 * 1.02841) / U1)**0.5.
    4. 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.
  5. Calculate L and store the result in worksheet constant named L1.
    1. Choose Calc > Calculator.
    2. In Store result in variable, enter K2.
    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 32.
    8. Choose Input column and enter K2.
    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 ((32 * 1.02841) / L1)**0.5.
    4. 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.

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