# Equivalence testing with TOST and a justified SESOI

Decision workbook and teaching example · 2026-10-06

The completed case is fictional. Its values and decisions are not actual findings; complete your project using relevant permissions, methods and requirements.

- Project: ____________________
- Researcher and role: ____________________
- Date and version: ____________________
- Data seen before the decision: ____________________
- Aim and scope: ____________________

## Completed example

| Stage/decision | Example | Check or action |
| --- | --- | --- |
| Question | An effect smaller than ±0.5 points | Justify actual units and SESOI. |
| Estimate | 0.20 with SE=0.15 | Obtain a design-appropriate SE. |
| CI90 | [−0.047,0.447] | Check the whole interval against bounds. |
| Low precision | Same estimate with SE=1 | Do not infer absence from uncertainty. |
| Report | p_TOST≈0.0228 in normal example | State method, bounds and limits. |

## Complete your own record

| Topic | Actual decision and reason | Evidence link and status |
| --- | --- | --- |
| Question | __________ | __________ |
| Estimate | __________ | __________ |
| CI90 | __________ | __________ |
| Low precision | __________ | __________ |
| Report | __________ | __________ |

## Completion checks

- [ ] A prospective SESOI rationale and test plan.
- [ ] Reproducible intervals and both one-sided p-values.
- [ ] A difference/equivalence report with uncertainty and limits.

## Changes and limitations

| Date | Change | Data known at decision time | Reason | Consequence for claim | Reviewer |
| --- | --- | --- | --- | --- | --- |
| __________ | __________ | __________ | __________ | __________ | __________ |

## Sources and further reading

- [Lakens (2017) — Equivalence Tests: A Practical Primer](https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)
- [American Statistical Association — Statement on p-values](https://www.amstat.org/asa/files/pdfs/p-valuestatement.pdf)
- [Pew Research Center — Writing Survey Questions](https://www.pewresearch.org/writing-survey-questions/)

Related guide: https://didgar-research-site1.vercel.app/en/guides/equivalence-testing/