Equivalence test calculator
Test whether a difference lies inside equivalence margins you set in advance, using two one-sided tests (TOST). Works with two groups, paired or one-sample data, or two proportions.
Runs locally in your browser; nothing is uploaded. Group sizes are whole numbers of at least 2 (at least 1 for proportions), SDs are greater than zero, alpha is from 0.0001 to 0.4999 and the lower margin must be below the upper margin. Raw CSV uses the exact headers group,value or before,after or value, with no blank cells, up to 10,000 rows and 1,000,000 characters; it is not available for two proportions. Downloads: a JSON report and a CSV result row. Use the fields for summaries, or choose Raw CSV values to paste data. Up to 1,000,000 characters. Review the settings before running.
Your result
How to use Equivalence test calculator
- Choose the design and whether you have summary statistics or raw CSV values.
- Enter the lower and upper margins you fixed before seeing the data, and alpha.
- Enter the summaries, or paste the CSV.
- Calculate, compare the 1 - 2 alpha interval with the margins, and download the report.
Useful next steps
How TOST works
Two one-sided tests check that the difference is above the lower margin and below the upper margin (Schuirmann 1987, J Pharmacokinet Biopharm 15:657; Lakens 2017, Social Psychological and Personality Science 8:355). The TOST p-value is the larger of the two one-sided p-values. Equivalence is declared when it is below alpha, which is the same as the 1 - 2 alpha confidence interval lying inside the margins, so alpha 0.05 uses a 90 percent interval.
Designs
Two groups use Welch's t by default, or Student's t if you assume equal variances. The difference is group 1 minus group 2; with raw CSV, group 1 is the first group label listed and the report names both groups, so set asymmetric margins with that order in mind. Paired data use the mean and SD of the differences, before minus after for raw CSV. One sample compares the mean minus a reference value with the margins. Two proportions use the difference with an unpooled Wald standard error, which needs reasonably large groups.
Limits
Margins must be justified and fixed before the data are seen. A nonsignificant ordinary test does not show equivalence, and a failed TOST does not show a difference.