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Basic Analysis > Oneway Analysis > Equivalence Tests
Publication date: 11/10/2021

Equivalence Tests

Equivalence tests are useful when you want to detect differences in means that are of practical interest. You must specify a threshold difference for which smaller differences are considered practically equivalent. In other words, if two group means differ by this amount or less, you are willing to consider them equivalent.

See Example of an Equivalence Test.

Equivalence Tests Report

Once you have specified the threshold value and variance assumption, the Equivalence Tests report appears. The full title of the report is Equivalence Tests with Pooled Variance or the Equivalence Tests with Unequal Variances, depending on the specified variance assumption. The specified threshold value implies upper and lower bounds, which are shown at the top of the report. The top of the report also contains the α level of the equivalence tests. The report consists of a table that contains the equivalence tests and a scatterplot that displays them. The equivalence tests and confidence intervals are based on Student’s t critical values.

Tip: To change the α level of the equivalence tests, use the Set α Level option in the Oneway Analysis red triangle menu before you select the Equivalence Tests option.

The red triangle menu next to Equivalence Tests with Pooled Variance or Equivalence Tests with Unequal Variances contains the following options:

Equivalence TOST Tests

Shows or hides the Equivalence TOST Tests report.

Equivalence Tests Scatterplot

Shows or hides the Equivalence Tests Scatterplot report.

Equivalence Tests Pairwise Comparisons

Shows or hides the Practical Equivalence reports for all pairwise comparisons.


Removes the Equivalence Tests report from the Oneway Analysis report window.

Equivalence TOST Tests

The Two One-Sided Tests (TOST) method is used to test for a practical difference between the means (Schuirmann 1987). Two one-sided t tests using the specified variance assumption are constructed for the null hypotheses that the true difference exceeds the threshold values. If both tests reject, the difference in the means does not statistically exceed either threshold value. Therefore, the groups are considered practically equivalent. If only one or neither test rejects, then the groups might not be practically equivalent.

For each comparison, the Equivalence TOST Tests report gives the following information:


Estimated difference in the means.

Std Error of Difference

Estimated standard error of the difference in the means.

Lower Bound t Ratio, Upper Bound t Ratio

Lower and upper bound t ratios for the two one-sided pooled-variance significance tests.

Lower Bound p-Value, Upper Bound p-Value

p-values corresponding to the lower and upper bound t ratios.

Maximum p-Value

Maximum of the lower and upper bound p-values.

Lower and Upper

Limits for a 12α confidence interval for the difference in the means.

Equivalence Tests Scatterplot

Using colors, this scatterplot indicates which means are practically equivalent and which are not practically equivalent as determined by the equivalence test. This plot is sometimes called a diffogram or a mean-mean scatterplot.

The plot shows a solid reference line on the diagonal as well as a shaded reference band. The width of the band is twice the practical difference. The coordinates of the point on the line segment are the means for the corresponding groups. There is an implied third axis on the diagonal where each line segment corresponds to a 12α confidence interval for a pairwise comparison. Hover over one of these points to show a tooltip that indicates the groups being compared and the estimated difference. When a line segment is entirely contained within the diagonal band, it follows that the means are practically equivalent.

The Equivalence Tests Scatterplot has the following option:

Show Reference Lines

Displays 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 better to hover over the points to view the labels.

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