What it means
A label used when a result passes a chosen statistical threshold, often p < 0.05. It does not show how large or useful an effect is. A result that is not statistically significant does not prove there is no effect.
Examples on this page are illustrations, not findings from the research cards.
Worked example
A study reports p = 0.03 against a 0.05 threshold. It passes that test, but the effect could still be too small to matter.
Hypothetical example: researchers choose p < 0.05 as their threshold. A test reports p = 0.03, so it passes. Under the tested model, including its no-effect assumption, results at least this extreme would occur about 3 times in 100 repetitions. This is not a 3% probability that the hypothesis is true or that chance caused the result.
If the estimated improvement were only one extra minute of activity per week, passing the threshold would not make that improvement large. If another test reported p = 0.08, it would not pass the same threshold, but that alone would not establish no effect. The estimate, uncertainty and study design still matter.
A closer look
A result is called statistically significant when it passes a chosen statistical threshold, often p < 0.05. For a test of no effect, the p-value asks: assuming no effect and the test's other assumptions, how often would results at least as extreme as this occur? A small p-value suggests the data are less compatible with those assumptions together. It is not the probability that the no-effect hypothesis is true.
Significance does not measure how large or useful an effect is, prove that a programme caused it, or guarantee that the analysis was sound. Researchers must also consider the effect estimate, its uncertainty and the study design. A result above the threshold can still be compatible with meaningful effects; not statistically significant does not mean the effect is zero.
A common misunderstanding
Statistical significance does not establish an important or causal effect; a non-significant result does not establish zero effect.
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Sources
The wording and examples are original explanations informed by these references.
- American Statistical Association · Statement on p-values ↗
- American Statistical Association · Official statement announcement ↗
Cite this explanation
Statistically significant. aikyam school. https://aikyam.school/glossary/statistically-significant/
Used in these cards
143 cards use this term
The original research wording is preserved in these cards.
