Statistics

What a p-value does and does not tell you

A p-value describes how unusual a result at least as extreme as the observed result would be under a specified statistical model. It is not the probability that a hypothesis is true.

Web edition · 14 October 2026

Do not put the entire judgement into one number

The ASA statement explains that a p-value does not measure effect size or scientific importance. Passing a threshold does not remove problems with research design, measurement or reporting. A small difference may be statistically clear in a large sample. Failing to find a significant result in a small sample does not establish that no difference exists.

Expand the statement of results

Before “p < 0.05”, explain the comparison and effect: which groups, which measurement and which units? Then add uncertainty and the analysis approach. Selecting only positive results for reporting prevents readers from seeing the actual research process.

A checking card

  1. Were the hypothesis and analysis specified in advance?
  2. How many different comparisons were made?
  3. Are the effect size and uncertainty reported?
  4. Are excluded data and analysis decisions explained?
  5. Could the result be tested with another design or dataset?

This card does not produce a quality score. It makes missing information visible and provides a starting point for rereading the methods and supplementary materials.

Sources and provenance

Source check / web edition: 14 October 2026. Historical documents retain their own original dates.