A p-value is the probability of seeing a result at least as extreme as yours if the null hypothesis were true, that is, if there were no real effect in the wider population. A small p-value means your sample result would be unlikely under that assumption, so you treat the effect as statistically significant. A p-value is not the probability that your hypothesis is true, and it is not a measure of how large the effect is; it only tells you how surprising the data are if nothing is going on.
What the threshold actually decides
The familiar cut-off of .05 is a convention, not a law of nature. It sets your tolerance for a false positive, the risk of declaring an effect that is not really there. Choosing alpha of .05 means you accept a one-in-twenty chance of that error before you ever see the data. Some fields demand a stricter .01 because the cost of a wrong claim is higher. The threshold is a decision rule you commit to in advance; moving it after you see the result is one of the surest ways to lose your supervisor's trust in your dissertation.
What the p-value actually means in practice
Strip away the jargon and a p-value answers one narrow question: if there were truly no effect, how often would chance alone hand you a result this striking or more so? A value of .02 says such data would turn up about twice in a hundred runs of a world where nothing is happening, which is rare enough that you doubt the "nothing is happening" story. It is a measure of surprise under the null hypothesis, not a verdict on your own hypothesis.
That framing keeps you honest about direction. A small p-value pushes you to reject the null, but it never confirms the specific alternative you hoped for, and it says nothing about why the effect appears, which is the job of careful design and the logic in why correlation is not causation. If you want to check a value against the test statistic and degrees of freedom you already have, the p-value calculator returns the exact figure.
The 0.05 significance threshold and where it came from
The .05 line is a historical convention, popularised by Ronald Fisher as a convenient marker, not a boundary nature respects. There is no real difference in evidence between a p-value of .049 and one of .051, yet the threshold treats them as opposite verdicts, which is exactly why reporting the exact value matters more than the pass-or-fail flag. Some disciplines have moved to .005 for new claims, and others use .01 when a false positive is costly.
The threshold also interacts with how many tests you run. Test twenty unrelated hypotheses at alpha of .05 and you should expect one to clear the line by chance alone, which is why corrections formultiple comparisons exist and why fishing through your data for any significant result is so risky. Set and justify your threshold in advance, as part of the move from describing data to inferring from it, and treat it as a commitment rather than a dial to turn after the fact.
p-value vs effect size: significance versus magnitude
These two numbers answer different questions and you need both. The p-value tells you whether an effect is likely to be real; the effect size tells you how big it is. Because significance depends so heavily on sample size, a large study can return a tiny p-value for a difference far too small to matter in practice, while a small but well-designed study can show a large effect that just misses the threshold. Reading the p-value alone, in either case, leads you to the wrong conclusion.
The fix is to report them side by side and interpret the pair. A significant result with a meaningful effect size is the strong outcome; a significant result with a trivial effect size is a statistical curiosity, not a finding. For the metrics and benchmarks that quantify magnitude, see how effect size is measured, and for a sense of how large a difference is in plain units our free effect size tool converts your figures into Cohen's d.
What a p-value does not tell you
The most common misreadings cost marks. A p-value of .04 does not mean there is a ninety-six percent chance your hypothesis is correct, and a p-value of .20 does not prove the null hypothesis is true; it only means you lack the evidence to reject it. Crucially, significance is not size. With a large enough sample, a trivial difference will cross the threshold, which is why a p-value must always be reported next to an effect size that shows how big the effect is. The p-value answers "is it likely real?", never "does it matter?".
Reporting the value honestly
Report the exact p-value rather than just "p < .05" wherever you can, because a value of .049 and a value of .003 carry very different weight even though both clear the threshold. Treat a result of .055 as what it is, just over the line, and discuss it as suggestive rather than dressing it up as significant. Pairing the p-value with a confidence interval for the effect gives the reader far more than a bare significance flag, and the formatting rules for all of these numbers live in how to report statistics in APA style.
| p-value | How to read it |
|---|---|
| Below .01 | Strong evidence against the null hypothesis |
| Below .05 | Conventionally significant; report the effect size too |
| Around .05 to .06 | Borderline; describe as suggestive, not significant |
| Above .10 | No evidence to reject the null; not proof it is true |
Where the p-value sits in your analysis
A p-value is the last step of an inferential test, not the whole story. It arrives only after you have chosen the right test, checked its assumptions, and computed a test statistic, which is the path traced in the move from descriptive to inferential statistics. Read in that context, the p-value becomes a disciplined yes-or-no on a single, pre-stated question rather than a magic number. Reported alongside its effect size and confidence interval, it gives your results chapter the honesty examiners reward.