Key points at a glance
- A non-significant finding does not prove an exactly absent effect.
- Report the estimate, uncertainty and sample regardless of the p-value.
- Do not silently rewrite the analysis or hypothesis afterwards.
What does the result actually say?
When a test does not cross the chosen significance threshold, that procedure has not found sufficient evidence against its tested null hypothesis. This does not logically establish that the true difference is exactly zero. Data quality and estimate precision matter to interpretation too.
The American Statistical Association cautions against threshold-only interpretation. Report the planned analysis and its findings fully, even when they do not meet the expected direction or cut-off.
An original example with two possible outcomes
Imagine an invented study estimating a two-point group difference. A wide 95% confidence interval from minus four to plus eight points includes negative and positive differences. “There is no difference” claims more than these data support.
A narrow interval from minus 0.2 to plus 0.2 points indicates different uncertainty. Whether these magnitudes are practically negligible depends on the scale and a justified relevance boundary set beforehand. Even here, an ordinary non-significant test does not by itself formally demonstrate equivalence.
Separate planned and additional analyses
First check that cleaning, coding and model implementation were correct. Correct documented errors regardless of whether the change makes the result more favourable. Do not keep trying subgroups or thresholds until a small p-value appears.
Additional analyses can be useful when justified and clearly labelled as developed after seeing the data. State what they investigate and the choices made along the way. A later explanation must not be presented as an original prespecified hypothesis.
Consider sample size, missing observations and suitable effect measures as well. Limited precision can arise from small or incomplete data. Stronger wording cannot repair it.
Keep reporting and interpretation distinct
In the results, present the test, estimate, interval, p-value where planned and relevant sample sizes. In the discussion, explain which interpretations fit the uncertainty and prior research. Unexpected findings can still inform the field when their limits are stated openly.
For the invented wide interval, you might write: “The analysis does not provide a precise estimate of the difference; the data are compatible with both negative and positive values.” Add the actual scale and study context.
Final submission context
Formal details can feel like a separate writing task, but they matter just as much for a printed submission. Anything missing, misplaced or inconsistently formatted in the document will also appear in the bound copy.
Use this guide together with your cover page, table of contents, page numbers, source notes and appendices. Prepare the final PDF for printing and binding only after the complete file has been checked.
Practical check before PDF export
- Do headings, chapter structure and page numbers match?
- Are sources, figures and tables included completely?
- Are required elements such as declarations, appendices or the cover page included where required?
- Did you open and check the final PDF after exporting it?
Checklist
- Report the planned analysis in full.
- Show the estimate and uncertainty.
- Check sample size and data problems.
- Identify exploratory analyses clearly.
- Match conclusions to the precision of the evidence.
Common mistakes
- Calling non-significance proof of equivalence.
- Reporting only favourable subgroups.
- Rewriting the original hypothesis after seeing the data.
Print and bind your finished thesis
Once you have checked the content and final PDF, configure the printed copies to match your submission requirements.
Configure printing and bindingRelated content
Explore related guidance on thesis structure, sources, formatting and final submission.
Frequently asked questions
Is a non-significant finding worthless?
No. It can limit an expectation or inform future study design. Its contribution depends on design, precision and data quality.
Can I say my hypothesis was rejected?
Follow the exact test logic and disciplinary conventions. A non-significant test does not simply establish the opposite claim. Describe the evidence available and what remains uncertain.
When can I claim equivalence?
You need an appropriate question, a substantively justified boundary defined in advance and a suitable procedure. Failure to find significance in an ordinary difference test is insufficient.