What Does p < 0.05 Mean? A Simple Guide to P-Values

Most introductory statistical tests begin with a null hypothesis. The null might say that there is no difference between two groups, no association between two variables or no effect of an intervention.

The p-value asks a narrower question:

If the null hypothesis and the assumptions of the statistical model were correct, how compatible are the observed data with that model?

Smaller p-values indicate greater incompatibility between the observed data and the tested null model.

So if your analysis gives p = 0.032, a useful plain-language interpretation is:

Under the null hypothesis and the statistical assumptions used, results at least as incompatible with the null as those observed would be relatively unusual.

That is less dramatic than “my hypothesis has been proved.”

It is also more accurate.

No.

This is one of the most common p-value errors.

A p-value of 0.032 does not mean:

“There is a 3.2% probability that the null hypothesis is true.”

It also does not mean:

“There is a 96.8% probability that my alternative hypothesis is correct.”

The conventional p-value is calculated under an assumption about the null hypothesis. It does not calculate the probability that the hypothesis itself is true.

The American Statistical Association has specifically warned against this interpretation.

Also no.

Suppose:

Study A finds a 0.2-point improvement on a 100-point score, with p < 0.001.

Study B finds a 5-point improvement, with p = 0.06.

Which finding matters more?

You cannot answer from the p-values.

Statistical significance is affected by the magnitude of the effect, variability, sample size and the statistical model. A very large study can produce a tiny p-value for a very small effect. A smaller study can produce a larger p-value while its data remain compatible with effects that would matter in practice.

That is why you should ask:

• How large is the estimated effect?
• How precise is it?
• What values are compatible with the confidence interval?
• Would that magnitude matter clinically, socially or programmatically?
• Was the study designed well enough for the estimate to be credible?

Statistics cannot decide importance on your behalf.

The 0.05 threshold is a convention. It is not a scientific law.

Many fields use 5% as a pre-specified significance level, which makes p < 0.05 a familiar decision rule. But treating 0.05 as a hard border can produce absurd interpretations.

Consider:

• p = 0.049
• p = 0.051

It is difficult to defend the idea that the first result represents a scientific discovery while the second represents no evidence at all.

The numbers are extremely close.

At minimum, look at the estimate and its uncertainty.

For example:

Contraceptive uptake was 12 percentage points higher in the intervention group than in the comparison group (95% CI 4 to 20 percentage points; p = 0.032).

Now the reader can see:

1. Direction: uptake was higher in the intervention group.
2. Magnitude: the estimated difference was 12 percentage points.
3. Uncertainty: the confidence interval ranged from 4 to 20 percentage points.
4. Hypothesis-test information: p = 0.032.

Then consider the study itself. A small p-value cannot rescue poor measurement, selection bias, inappropriate modelling or a badly designed comparison.