Methods and formulas for comparisons with a control for mixed effects models in Comparisons

Select the method or formula of your choice.

Dunnett method for comparisons with a control in a mixed effects model

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.

Note

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.

Critical value

The critical value has the following expression:
For more information on Dunnett's method, see the following references:
  1. 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.
  2. J.C. Hsu (1996). Multiple Comparisons: Theory and methods. Chapman & Hall.
TermDescription
the upper percentile of the distribution that Dunnett proposes with comparisons and df degrees of freedom
αthe simultaneous probability of making a Type I error
kthe number of levels in the fixed effect term or the random term
dfthe 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.

Fisher method for comparisons with a control in a mixed effects model

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.

Note

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.

Critical value

For an upper bound or a lower bound, the critical value has the following expression:
For a two-sided confidence interval, the critical value has the following expression:
TermDescription
the quantile from the student's t distribution with df degrees of freedom
αthe individual probability of making a Type I error
dfthe 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.

Bonferroni method for comparisons with a control in a mixed effects model

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.

Note

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.

Critical value

For an upper bound or a lower bound, the critical value has the following expression:
For a two-sided confidence interval, the critical value has the following expression:
TermDescription
the upper percentile of the student's t distribution with df degrees of freedom
αthe simultaneous probability of making a Type I error
c
kthe number of levels in the fixed effect term or the random term
dfthe 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.

Sidak method for comparisons with a control in a mixed effects model

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.

Note

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.

Critical value

For an upper bound or a lower bound, the critical value has the following expression:
The critical value has the following expression:
TermDescription
the upper percentile of the student's t distribution with df degrees of freedom
αthe simultaneous probability of making a Type I error
c
kthe number of levels in the fixed effect term or the random term
dfthe 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.

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy