The two-sided 100(1 − α
) confidence interval for the difference of means has the following expression:
For multiple comparisons with a control, Minitab also calculates one-sided intervals.
- Upper bound
- Lower bound
For more information on how to calculate the fitted means and the standard error of the difference, go to Methods and formulas for fitted means in Fit Mixed Effects Model.
Calculations for the test statistic, adjusted p-value, individual confidence level, and grouping information table match the calculations for general linear models. For more information, go to the Methods and Formulas for comparisons for general linear models.
The critical value has the following expression:
For more information on Dunnett's method, see the following references:
- Dunnett, C. W. (January 01, 1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50, 1096-1121.
- J.C. Hsu (1996). Multiple Comparisons: Theory and methods. Chapman & Hall.
|the upper percentile of the distribution that Dunnett proposes with comparisons and df degrees of freedom|
|α||the simultaneous probability of making a Type I error|
|k||the number of levels in the fixed effect term or the random term|
|df||the degrees of freedom|
The degrees of freedom depend on whether the comparison is for a fixed effect term or a random term.
Degrees of freedom (df)
For a fixed effect term, the degrees of freedom (df) are the same as the degrees of freedom for testing the corresponding fixed effect term. For a random term, the degrees of freedom use Satterthwaites approximation method.
For more information on the calculation of the degrees of freedom, go to Methods and formulas for tests of fixed effects in Fit Mixed Effects Model.