Scientific Decisions After p>0.05: Uncertainty, Confidence Intervals and Next Steps
A p value above 0.05 does not prove that there is no effect. Learn how to interpret effect sizes, confidence intervals, precision and study limitations.
What does p>0.05 actually mean?
A p value above 0.05 means that the observed data do not clearly contradict the null model under the assumptions of the analysis. It does not prove that there is no effect, that two groups are identical, or that the study has failed. A p value alone does not describe the magnitude, clinical importance or reproducibility of an effect.
Suppose the estimated treatment difference is 4 units, with a 95% confidence interval from −1 to 9 and p=0.11. These data are compatible with both a small adverse effect and a potentially important benefit. The defensible conclusion is that the estimate is imprecise—not that there is no difference.
Start with the effect estimate and confidence interval
Ask three questions together:
What is the point estimate?
Which values are compatible with the confidence interval?
How do those values compare with a clinically meaningful threshold?
A narrow interval restricted to clinically trivial values may provide evidence against an important effect. A wide interval indicates unresolved uncertainty. In either case, classifying the study only by whether p crossed 0.05 discards useful information.
Non-significance is not equivalence
A non-significant superiority test does not establish equivalence. Equivalence and non-inferiority require prespecified clinical margins and an appropriate design and analysis. When equivalence is the objective, the confidence interval must be evaluated against those margins, commonly through the two one-sided tests framework.
Do not automatically blame sample size
It is tempting to explain a non-significant result by saying that the sample was too small. Observed or post-hoc power calculated from the same data should not be used to support that claim because it largely restates the p value. Report the width of the confidence interval, the prospective sample-size calculation, actual recruitment and attrition instead.
Practices to avoid
Repeatedly changing analyses until p falls below 0.05.
Removing outliers solely to achieve significance.
Presenting unplanned subgroup analyses as confirmatory evidence.
Calling p=0.051 “almost significant” while treating p=0.049 as definitive.
Writing “there was no association” solely because p>0.05.
Exploratory analyses can be useful, but they should be labelled as exploratory and confirmed in independent data.
How should the result be reported?
Weak: “There was no difference between groups (p=0.12).”
Better: “The mean difference was 3.2 units (95% CI −1.9 to 8.3; p=0.12). Because the interval includes both a small adverse effect and a potentially meaningful benefit, the result remains inconclusive.”
Practical checklist
Check data quality and model assumptions.
Report the effect estimate and 95% confidence interval.
Compare the interval with a prespecified clinically important difference.
Assess multiplicity and selective-reporting risks.
Evaluate the influence of missing data and attrition.
Preserve the distinction between absence of evidence and evidence of absence.
Plan any future study prospectively around a meaningful target effect.
Frequently asked questions
Is p=0.06 almost significant?
No. The 0.05 threshold is not a scientific cliff. Interpret the p value continuously and alongside the effect estimate and uncertainty.
Can a non-significant study be published?
Yes. A well-designed, transparently reported study can be informative regardless of whether a threshold is crossed. Precision and limitations must be stated clearly.
Can I recruit more participants after seeing the result?
Unplanned optional stopping can inflate the false-positive rate. Interim analyses or adaptive rules must be prespecified and analysed appropriately.
References
Wasserstein RL, Lazar NA. The ASA Statement on p-Values. 2016.
Greenland S et al. Statistical tests, P values, confidence intervals, and power. 2016.
Wasserstein RL, Schirm AL, Lazar NA. Moving to a World Beyond “p<0.05”. 2019.
Accessed 20 June 2026. This article provides general methodological information and does not replace a study-specific statistical analysis plan.