A p-value is the probability of seeing a result as extreme as yours if there were actually no real effect — so a small p-value (usually below .05) suggests your finding is unlikely to be a fluke. If you're staring at "p = .03" in your output and quietly panicking about what it actually means for your thesis, you're in the right place — most people are never taught this clearly.
Key Takeaways
- A p-value measures surprise, not truth. It tells you how surprising your data would be if there were no real effect — not the probability that your hypothesis is correct.
- The common cutoff is p < .05, meaning less than a 5% chance the result happened by random luck alone; below this, results are usually called "statistically significant."
- A small p-value does not mean a large or important effect — always report an effect size (like Cohen's d or η²) alongside it.
- P-values depend on sample size: with enough participants, even a trivial difference can produce a tiny p-value.
- In APA 7 format, p is italicised with no leading zero (e.g. p = .03, not p = 0.03).
What is a p-value, really?
A p-value answers one specific question: "If there were truly no effect or difference in the real world, how likely is it that I'd get data at least this extreme just by chance?" That's it. It's a measure of how well your data fit a boring "nothing is happening" scenario called the null hypothesis.
Think of it like a courtroom. The null hypothesis is the assumption of innocence: "there's no real difference between these two groups." Your data is the evidence. The p-value tells you how surprising that evidence would be if the defendant (the null) were actually innocent. A very small p-value means the evidence is so surprising under innocence that you start to doubt it.
The key mental shift: a p-value is not the probability that your hypothesis is true. It's the probability of your data, assuming the null is true. Getting these backwards is the single most common statistics mistake in student papers.
What counts as a "significant" p-value?
By convention, a result is called statistically significant when p is less than .05 — meaning there's under a 5% probability the result is due to random chance. This threshold is called alpha (α), and .05 is simply the most widely used cutoff, not a law of nature.
Here's how to read common values:
| P-value | Plain-English meaning | Typical label |
|---|---|---|
| p = .60 | Very consistent with "no effect" | Not significant |
| p = .08 | Suggestive, but doesn't clear the bar | Not significant (marginal) |
| p = .04 | Unlikely under "no effect" | Significant |
| p = .002 | Very unlikely under "no effect" | Highly significant |
Some fields (like particle physics or genetics) use far stricter thresholds. In psychology and the social sciences, .05 remains standard, though many researchers now argue for reporting exact p-values and effect sizes rather than fixating on the cutoff.
A worked example with real numbers
Imagine you're testing whether a new study technique improves exam scores. You run an independent-samples t-test comparing 30 students who used the technique against 30 who didn't.
Your output shows:
t(58) = 2.45, p = .017, Cohen's d = 0.63
Let's decode each piece:
- t(58) = 2.45 — the test statistic. The 58 is your degrees of freedom (roughly your total sample minus the number of groups). The 2.45 measures how far apart the two group means are, relative to the noise in the data.
- p = .017 — there's about a 1.7% chance you'd see a difference this large if the study technique actually did nothing. Since .017 is below .05, the result is statistically significant.
- Cohen's d = 0.63 — the effect size. This says the difference is medium-to-large in practical terms, not just statistically detectable.
The p-value alone would tell you the effect is unlikely to be chance. The effect size tells you it also matters. You need both — a point we'll come back to, because it's where most beginners stop too early.
Why a small p-value doesn't mean a big effect
A p-value tells you whether an effect exists, not how large or important it is. This trips up almost everyone. With a large enough sample, a difference so tiny it's meaningless — say, a 0.2-point difference on a 100-point exam — can produce p < .001.
That's why journals following APA 7 now require an effect size alongside every significance test. If a colleague tells you "it was significant, p = .04!" your next question should always be: "significant, sure — but how big is the effect?"
This is also why StatRyx automatically reports the relevant effect size (Cohen's d, η², or r) next to every p-value it calculates — so you never accidentally present a trivial finding as an important one.
What a p-value does NOT tell you
Being precise here is what separates a confident write-up from a shaky one. A p-value does not tell you:
- The probability your hypothesis is true. p = .03 does not mean "97% chance my theory is right."
- The probability the result was due to chance in the real world. It's the probability of the data under the null, not the probability of the null itself.
- That the effect is large or practically meaningful. (See above — that's what effect sizes are for.)
- That a non-significant result proves there's no effect. p = .30 means you failed to find evidence of an effect, not that you proved the null true. Absence of evidence isn't evidence of absence.
How do I report a p-value in APA 7 format?
In APA 7, italicise the p, drop the leading zero, and report exact values to two or three decimals (e.g. p = .03), unless the value is below .001, in which case write p < .001. Never write "p = 0.030" or "p = .000."
Correct examples:
- t(58) = 2.45, p = .017, d = 0.63
- F(2, 42) = 4.31, p = .019, η² = .17
- r(48) = .34, p = .015
Always pair the p-value with the test statistic, degrees of freedom, and an effect size. If you're unsure which test produces which notation, our guide on choosing the right statistical test walks through it.
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Frequently Asked Questions
Does a p-value of .05 mean my result is 95% likely to be true?
No. This is the most common misunderstanding. A p-value of .05 means there's a 5% chance of seeing data this extreme if the null hypothesis were true — it says nothing directly about the probability that your hypothesis is correct. The p-value is about the data, not about the truth of your theory.
Is a p-value of .06 useless?
Not useless, just not below the conventional .05 threshold. A result at p = .06 is often described as "marginal" or "approaching significance," though strict reviewers may reject that phrasing. The honest approach is to report the exact value and the effect size, then let readers judge — a moderate effect with p = .06 in a small sample may simply need more data.
What's the difference between a p-value and an effect size?
A p-value tells you whether an effect is likely to be real (not chance); an effect size tells you how big that effect is. You can have a significant p-value with a tiny, meaningless effect, especially in large samples. APA 7 requires reporting both, which is why StatRyx always shows them together.
Why do p-values get smaller with bigger samples?
Larger samples reduce random noise, making it easier to detect even small true differ