P-Value Greater Than 0.05: Meaning and Reporting Examples

A reporting sentence that follows this logic:

Participants in the intervention group had an estimated 25% lower risk of the outcome than those in the comparison group (RR 0.75, 95% CI 0.55-1.03; p = 0.08).

Your analysis gives:

p = 0.08

The first temptation is disappointment.

The second is usually worse:

“There was no association.”

That conclusion may be much stronger than your data allow.

A p-value above 0.05 tells you that the result did not cross a chosen significance threshold under the statistical test you used.

It does not tell you that nothing happened.

In a conventional hypothesis test, the p-value measures how compatible the observed data are with a specified statistical model, usually one that includes a null hypothesis.

If you prespecified a 5% significance level and obtain:

p = 0.08

the result does not meet the conventional p < 0.05 rule.

It is therefore often described as not statistically significant at the 5% level.

That is a statement about a testing threshold.

It is not proof that the null hypothesis is true.

Statistical significance depends on more than the estimated effect.

It also depends on factors such as:

• sample size;
• variability;
• event frequency;
• measurement precision;
• the statistical model;
• the chosen significance threshold.

A study can therefore produce a potentially important point estimate but remain too imprecise to rule out the null value.

This is one reason researchers should not reduce an entire result to:

significant / not significant.

Instead ask:

What effects remain compatible with the data?

That question moves you toward the confidence interval.

Consider two hypothetical studies.

Not in the dramatic way scientific writing sometimes suggests.

If 0.05 is your prespecified significance level, the two numbers fall on different sides of the formal threshold.

But they do not represent two entirely different universes of evidence.

Treating p = 0.049 as a meaningful discovery and p = 0.051 as “nothing” throws away the continuity of the evidence.

The threshold can serve a decision rule.

It should not become your entire interpretation.

The values fall on opposite sides of a p < 0.05 decision rule but do not represent a sudden transformation in evidence. Interpretation still requires the effect estimate, uncertainty, study design and assumptions. Values are illustrative; the displayed axis is magnified.

Not necessarily.

A non-significant p-value alone cannot diagnose the reason.

A wide confidence interval may indicate limited precision, which can arise partly from a small sample, high variability or few events.

But automatically responding to p > 0.05 with:

“I needed a larger sample”

can become retrospective reasoning based on the result you wanted.

Sample-size planning should be justified before the analysis, based on the study objective, desired precision or power and defensible assumptions.

No.

Showing that a conventional superiority test is not statistically significant is not the same as demonstrating that two treatments, groups or conditions are equivalent.

Equivalence and non-inferiority questions require designs and decision rules built for those purposes.

“No statistically significant difference” should not be silently upgraded to “the groups are the same.”

Where to go next: A large p-value is not evidence of no effect. See what the interval adds in how to interpret a 95% confidence interval and how the three numbers work together in p-values, confidence intervals and effect sizes.