In the Oneway platform, the options in the Equivalence Test submenu enable you to test means or standard deviations. A specification window enables you to select between a t test and a Wilcoxon test for equivalence, superiority, or noninferiority. The equivalence test reports contain plots and summary tables.
For equivalence tests, the two one-sided tests (TOST) method is used to test for practical equivalence between the means or the ratio of two standard deviations. For equivalence tests about means, see Schuirmann (1987). Two one-sided tests are constructed for the null hypotheses that the true difference or true ratio exceeds the threshold values. If both tests reject, the difference in the means or ratio does not statistically exceed either threshold value. Therefore, the groups are considered practically equivalent. See Example of an Equivalence Test.
Note: When there are multiple comparisons being performed in an equivalence, superiority, or noninferiority test, there is no alpha correction made for multiple tests.
Selecting an equivalence test option in the Equivalence Tests submenu launches a window that enables you to define your test.
Type of Test
Specifies the test type.
t-Test
Specifies a t test.
Wilcoxon Test
Specifies a Wilcoxon test.
Alternative Hypothesis
Defines the structure of the equivalence test.
Equivalence (Two-Sided)
Specifies an equivalence test. Use this option when the goal is to show that group differences are not bigger than the equivalence margin.
Superiority (One-Sided)
Specifies a superiority test. Use this option when the goal is to show that a group is superior, or better than, another group.
Noninferiority (One-Sided)
Specifies a noninferiority test. Use this option when the goal is to show that a group is not inferior to another group.
Side of the Alternative Hypothesis
(Available only for one-sided tests.) Specifies the direction of the alternative hypothesis.
Hypotheses Plot
Provides a graphical depiction of the hypothesis test.
Type of Comparisons
Defines the type of comparison to be performed.
All Pairwise
Specifies comparisons between all pairs of group levels.
With Control
Specifies comparisons of each level to a specified control level.
Variance Assumption
(Available only for t tests.) Defines the variance assumption used for the test calculations.
Pooled Variance
Specifies that calculations be based on a pooled variance. Use this option when variances are assumed equal across groups.
Unequal Variances
Specifies that calculations be based on unequal group variances.
Margin and Alpha
Defines the significance levels for the test.
Difference
(Available only for tests for means.) Specifies the equivalence, superiority, or noninferiority margin. This margin, or delta, is the difference that has practical significance. For equivalence tests, the difference must be greater than zero.
Ratio
(Available only for tests for standard deviations.) Specifies the equivalence, superiority, or noninferiority margin as a ratio of standard deviations. This margin defines a ratio in standard deviations that has practical significance. The range of values is defined as (Ratio, 1/Ratio). For equivalence tests, the ratio must be different from 1.
Alpha
Specifies the significance level for the test.
The test report begins with a description of the alternative hypothesis that is being tested. For each comparison, the Tests report contains the following columns:
Difference
(Available only for tests for means.) The estimated difference in the means for the t tests or the difference in the score means for the Wilcoxon tests.
Std Error of Difference
(Available only for t tests for means.) The estimated standard error of the difference in the means.
Ratio
(Available only for tests for standard deviations.) The estimated ratio of standard deviations.
Lower Bound t Ratio, Upper Bound t Ratio
(Available only for t tests for means. Only one bound appears for one-sided tests.) The lower or upper bound t ratios for the one-sided significance tests.
Lower Bound z Ratio, Upper Bound z Ratio
(Available only for Wilcoxon tests for means. Only one bound appears for one-sided tests.) The lower or upper bound z ratios for the one-sided significance tests.
Lower Bound F-value, Upper Bound F-Value
(Available only for tests for standard deviations. Only one bound appears for one-sided tests.) The lower or upper bound F ratios for the one-sided significance tests.
Lower Bound p-Value, Upper Bound p-Value
(Only one p-value appears for one-sided tests.) The significance probabilities (p-values) that correspond to the lower or upper bound t ratios.
Max p-Value
(Available only for equivalence tests.) Maximum of the lower and upper bound p-values.
Hodges-Lehmann
(Available only for Wilcoxon tests for means.) The Hodges-Lehmann estimate of the difference in group locations. Calculated as the median of all possible differences of two points, one from each group. This metric is used in the Forest Plot.
Two-Sided Lower 90%, Two-Sided Upper 90%
Limits for a 1−2α confidence interval for the difference in the means or the ratio of standard deviations.
Assessment
An assessment of the hypothesis test for the specified alpha level.
The Equivalence, Superiority, or Noninferiority Tests red triangle menu contains the following options:
Test Report
Shows or hides a report that summarizes the equivalence tests, superiority tests, or noninferiority tests for means or standard deviations. See Equivalence Tests Report.
Scatterplot
(Available only for t tests for means.) Shows or hides a scatterplot. The pairwise comparison confidence intervals are plotted on a scatterplot that is colored by acceptance regions. The intervals are plotted on a mean-mean scale with shading that indicates the equivalent, superior, or noninferiority regions. This plot is sometimes called a diffogram or a mean-mean scatterplot.
Tip: Hover over a point to show the groups being compared and the estimated difference.
The Scatterplot has the following option:
Show Reference Lines
Shows or hides reference lines for the points on the scatterplot. This is not recommended if there are many points in the scatterplot. If there are many points, it is recommended that you hover over the points to view the labels.
Forest Plot
Shows or hides a forest plot. The comparison confidence intervals are plotted versus the difference in means or ratio of standard deviations. The intervals are plotted on a difference of means or ratio of standard deviations scale. Shading indicates the equivalent, superior, or noninferiority regions.
Tip: Hover over a point to show the groups being compared and the estimated difference or ratio.
Pairwise Comparisons
(Available only for equivalence t tests for means.) Shows or hides the Practical Equivalence reports for all pairwise comparisons. In addition to the values provided in the Equivalence Tests Report, the report includes a visual representation of each paired test.
Remove
Removes the test report from the Oneway Analysis report window.