Tests_for_equal

Tests for equal variances

For the default parallel and 2x2 crossover models, some tests in Bioequivalence (e.g., the two one-sided t-tests) rely on the assumption that the observations for the group receiving the test formulation and the group receiving the reference formulation come from distributions that have equal variances, in order for the test statistics to follow a t-distribution. There are two tests in Bioequivalence that verify whether the assumption of equal variances is valid:

The Levene test is done for a parallel design that uses the default model (formulation variable with intercept included). See Snedecor and Cochran (1989) for more information.

The Pitman-Morgan test is done for a 2-period, 2-sequence, 2-formulation crossover design that uses either Variance Components or all fixed effects model. See Chow and Liu (2nd ed. 2000 or 3rd ed. 2009) for more information. In addition to the required column mappings, Sequence and Period must also be mapped columns.

For replicated crossover designs, the default model in Bioequivalence already adjusts for unequal variances by using Satterthwaite Degrees of Freedom and by grouping on the formulation in the repeated model, so a test for equality of variances is not done.

The results of the Levene test and Pitman-Morgan test are given in the Average Bioequivalence output worksheet and at the end of the Core Output. Both tests verify the null hypothesis that the true variances for the two formulations are equal by using the sample data to compute an F-distributed test statistic. A p-value of less than 0.05 indicates a rejection of the null hypotheses (and acceptance that the variances are unequal) at the 5% level of significance.

If unequal variances are indicated by the Levene or Pitman-Morgan tests, the model can be adjusted to account for unequal variances by using Satterthwaite Degrees of Freedom on the General Options tab and using a ‘repeated’ term that groups on the formulation variable as follows.

For a parallel design:

Map the formulation variable as Formulation.

Use the default Fixed Effects model (the formulation variable).

Use the default Degrees of Freedom setting of Satterthwaite.

Map the Dependent variable.

Map the Subject and Period variables as Classification variables.

If the data does not contain a Period column, a column that contains all ones can be added as the Period variable.

Set up the Repeated sub-tab of the Variance Structure tab as:

Repeated Specification: Period

Variance Blocking Variables (Subject): Subject

Group: Formulation

Type: Variance Components

For a 2x2 crossover design:

1. Map the Sequence, Subject, Period, Formulation, and Dependent variables accordingly.

2. Use the default model.

Fixed effects: Sequence + Formulation + Period

Random effects: Subject(Sequence)).

3. Use the default Degrees of Freedom setting of Satterthwaite.

4. Set up the Repeated sub-tab of the Variance Structure tab as:

Repeated Specification: Period

Variance Blocking Variables (Subject): Subject

Group: Formulation

Type: Variance Components