The modified Levene's test uses the absolute deviation of the observations in each treatment from the treatment median. It then assesses whether or not the mean of these deviations are equal for all treatments. If the mean deviations are equal, the variances of the observations in all treatments will be the same. The test statistic for Levene's test is the ANOVA F-statistic for testing equality of means applied to the absolute deviations.

You can do this in Minitab by making a new column where each value is the absolute value of the response minus the median of that treatment. Then perform a One-Way ANOVA using the new column as the response. The F-statistic and p-value will be the test statistic and p-value for Levene's test.

For example, suppose the responses are in C1 and the treatments are in C2, and C3-C6 are empty.

C1 | C2 |
---|---|

Responses | Treatments |

10 | 1 |

8 | 1 |

6 | 1 |

4 | 1 |

3 | 1 |

16 | 2 |

14 | 2 |

10 | 2 |

6 | 2 |

2 | 2 |

To perform Levene's test in Minitab for this data set:

- Choose .
- Click Both samples are in one column.
- In Samples, enter C1.
- In Sample IDs, enter C2. Click OK.

Test
Null hypothesis H₀: σ₁ / σ₂ = 1
Alternative hypothesis H₁: σ₁ / σ₂ ≠ 1
Significance level α = 0.05

Test
Method Statistic DF1 DF2 P-Value
Bonett 2.14 1 0.143
Levene 2.20 1 8 0.176

You can verify these calculations using One-Way ANOVA:

- Choose .
- In Variables, enter C1.
- In By variables (optional), enter C2.
- Click Statistics.
- Deselect all fields except Median.
- Click OK in each dialog box.
- Enter the treatment medians in C5.
C1 C2 C3 C4 C5 Responses Treatments ByVar1 Median1 Treatment Medians 10 1 1 6 6 8 1 2 10 6 6 1 6 4 1 6 3 1 6 16 2 10 14 2 10 10 2 10 6 2 10 2 2 10 - Choose .
- In Store result in variable, enter C6.
- In Expression, enter ABSO(C1-C5). Click OK.
- Choose .
- Choose Response data are in one column for all factor levels.
- In Response, enter C6.
- In Factor, enter C2. Click OK.

Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Treatments 1 12.10 12.100 2.20 0.176
Error 8 44.00 5.500
Total 9 56.10

When you examine the output you see that the F-statistic and p-value in the One-way ANOVA table are identical with the test statistic and p-value for Levene’s test.