What Does a P-Value Mean?

P-values settle more research arguments than almost any other number, and they’re also among the most misread. The misreading is common enough that the American Statistical Association published a formal statement on p-values to correct it, and the usual shorthand students learn is part of the problem.

Having coached 10,000+ students, we’ve found the confusion usually comes down to three things: what a p-value actually measures, what counts as significant, and what it can’t tell you. In this post, I’ll explain each in plain language, then show you how a real Master’s thesis reports its p-values, and how to report yours.

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What a p-value really tells you

When you run a statistical test, you start from a null hypothesis: the assumption that there’s no effect or no relationship between your variables. The p-value answers one question about it: if the null hypothesis were true, how likely is a result at least as extreme as the one you got? A small p-value means your data would be surprising in a world with no real effect.

That’s all it tells you. The ASA statement puts two common misreadings plainly: p-values “do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone”.

Let’s look at a practical example to make this a little more tangible.

Imagine you’re testing whether a new study technique improves exam scores. Your null hypothesis is that the technique makes no difference. If you get a p-value of 0.03, that means that if the technique really had no effect, you’d see a difference this large (or larger) only about 3% of the time. It doesn’t mean there’s a 97% chance the technique works, and it doesn’t mean there’s a 3% chance your result was a fluke.

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What counts as a significant p-value?

Before you analyze anything, you set a threshold called the significance level, or alpha. In most social science and health research it’s 0.05, meaning you’ll call a result statistically significant if the p-value falls below 0.05. One term you’ll meet in the table is effect size: a measure of how big a difference or relationship is. We’ll come back to it in the next section. Here’s how different p-values are usually read against that threshold:

p-value	At a 0.05 threshold	What it says about your data
Below 0.001	Significant	A result this extreme would turn up less than 0.1% of the time if there were no real effect
0.001 to under 0.01	Significant	Very unlikely under the null hypothesis: less than 1% of the time
0.01 to under 0.05	Significant	Unlikely under the null hypothesis, but check the effect size and how many tests you ran
0.05 to 0.10	Not significant	Somewhat unusual under the null hypothesis; report it as not significant rather than “nearly” significant
Above 0.10	Not significant	Not surprising under the null hypothesis, which is not the same as showing there’s no effect

The 0.05 threshold is a convention, not a law of nature. Some fields are stricter and use 0.01 or even 0.001, and many researchers now question whether 0.05 should remain the default at all.

The ASA statement goes further: conclusions “should not be based only on whether a p-value passes a specific threshold”. Instead, it says researchers should weigh “the design of a study, the quality of the measurements, the external evidence for the phenomenon under study, and the validity of assumptions that underlie the data analysis.” For your dissertation, that means reading your p-value alongside a few other things:

• How big the effect is, which is your effect size (more on that below).
• How well the study was designed: your sample size, how you sampled, and what you controlled for.
• How good your measures are: whether your instruments are validated and reliable.
• Whether your test’s assumptions hold: for example, normality or equal variances, if your test relies on them.
• What other studies found: whether your result fits the existing literature or contradicts it.

Many researchers also report a confidence interval, which shows the range of plausible values for the effect rather than a yes-or-no verdict.

When you’re writing your dissertation or thesis, find out which threshold your field uses and why, set yours before you look at the data, and say so in your methodology. Changing the threshold after you’ve seen the results is one of the fastest ways to lose an examiner’s trust.

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P-values don’t measure effect size

A small p-value doesn’t mean you’ve found something important. A p-value tells you about statistical significance, but it says nothing about practical significance, or effect size. With a large enough sample, a tiny and practically meaningless difference can produce p = 0.001. With a small sample, a large and important difference can miss 0.05 entirely.

That’s why you report an effect size alongside every p-value. Effect sizes tell your reader how big the difference or relationship is, and Jacob Cohen’s (1988) benchmarks are the usual starting point for reading them:

Effect size measure	Small	Medium	Large
Cohen’s d (difference between two groups)	0.2	0.5	0.8
Eta squared, η² (share of variance explained)	0.01	0.06	0.14
Pearson’s r (correlation)	0.1	0.3	0.5

One caution: SPSS reports partial eta squared, which matches eta squared only in a one-way design, so check which one you have before comparing it with these benchmarks. And treat the benchmarks as rough guides rather than rules. Cohen offered them for when nothing better is available, so if published studies in your field report typical effect sizes, compare yours with those instead.

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A real-world example of p-values

Here’s what this looks like in a real Master’s thesis in education. The study surveyed 100 university students of Japanese and compared their motivation across four reasons for taking the course: as a major, as a minor, as a requirement, or for fun. Watch how the passage reports three separate tests.

Three sentences, and they make three good moves. Let’s break them down:

The move	Where it happens
Reports the test, not just the p-value	“F [3, 94] = 4.821”. The test statistic and its degrees of freedom let a reader check the result rather than take the p-value on trust.
Adjusts for running three tests	“α = 0.017 Bonferroni corrected”. The 0.05 threshold is divided by the number of tests (0.05 ÷ 3), so the chance of a false positive across all three stays at or below 5%.
Reports effect sizes	“The effect sizes were all medium… η2 = 0.13”. Against Cohen’s benchmarks, values from 0.10 to 0.13 sit between medium (0.06) and large (0.14).

Notice the third result. The thesis rounds its corrected threshold to 0.017 (0.05 ÷ 3 is really 0.0167) and reports this p-value as 0.017 too. Rounded like that, the two numbers look identical. Working back from the reported F(3, 94) = 3.549, though, the exact p-value is about .0174, just above .0167. Strictly, this result doesn’t clear the corrected bar, even though the thesis counts it as significant.

That’s exactly why the effect size earns its place: η² = 0.10 tells your examiner how big the difference is, whichever side of the line the p-value falls. If you get a borderline result, report the exact p-value and the exact threshold, and lean on the effect size rather than rounding your way to significance.

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Common mistakes to avoid

One of the biggest mistakes is treating a p-value above 0.05 as proof that there’s no effect. A p-value of 0.06 doesn’t mean your hypothesis is false; it means your data don’t clear the bar you set. You might have a real effect that your study didn’t have enough statistical power to detect, often because the sample was too small. If that’s where you’ve landed, our article about results that aren’t statistically significant walks through what to do next.

Another is running many tests without adjusting your significance level. Each test at 0.05 carries a 5% risk of a false positive when there’s no real effect, and across many tests those risks compound: across 20 independent tests, the chance of at least one “significant” result by chance alone is about 64%. A correction such as Bonferroni, used in the example above, keeps that risk in check. Whatever you do, decide on your tests in advance and report all of them, not just the ones that came out significant.

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How to report a p-value

Many programs, especially in the social sciences, follow APA style for statistics, and its rules for p-values are short. The Purdue OWL’s APA guide summarizes the main ones:

• Report the exact value to two or three decimal places, such as p = .032.
• Below .001, write p < .001 rather than the exact number.
• Drop the leading zero, because a p-value can’t be greater than 1: p = .008, not p = 0.008.
• Italicize the p.

It follows that you should never write p = .000, even if your software shows it.

Then give your examiner the context around the number: the test statistic, its degrees of freedom, and an effect size. The second result in the example above, written in APA style, would read F(3, 95) = 4.21, p = .008, η² = .12. If you’re not sure which test produced your numbers in the first place, start with our guide to choosing the right statistical test.

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Context matters more than you think

The interpretation of any p-value depends on your research context. Your sample size, your design and your field all shape how strong a given result is. The same p-value can carry a lot of weight in a large, well-designed trial and very little in a small pilot study.

So read published studies and completed dissertations in your area before you analyze your data. See how other researchers report their p-values, which thresholds they use, and what effect sizes they treat as meaningful. If you’re still unsure what your study calls for, it’s the kind of question worth settling with your advisor, or in one-on-one stats coaching, before you run a single test.

Still have questions?

Is a p-value of 0.05 significant?

It sits exactly on the line, and textbooks differ on whether p ≤ 0.05 or p < 0.05 counts as significant. Rather than lean on the label, report the exact value alongside an effect size. A result that close to the threshold should be interpreted cautiously whichever way you call it.

Is a p-value of 0.001 statistically significant?

Yes, at the usual 0.05 threshold and at the stricter 0.01 one. It means a result at least that extreme would occur only about 0.1% of the time if there were no real effect. It still says nothing about how large or important the effect is, so report an effect size too.

Is 0.01 or 0.05 more significant?

A p-value of 0.01 means your results would be even less likely than at 0.05 if there were no real effect. As thresholds, 0.01 is the stricter one: fewer results clear it, so fewer false positives get through. Neither tells you how large or important an effect is.

What is a good p-value?

There isn’t one. A p-value is a result to report honestly, not a target to hit. Below your preset significance level, usually 0.05, a result is statistically significant. Chasing a “good” p-value by rerunning or reshaping analyses is called p-hacking, and examiners look for it.

What does the p in p-value stand for?

Probability. Specifically, it’s the probability of getting results at least as extreme as yours if there were no real effect (the assumption researchers call the null hypothesis), which is why a smaller p-value means your results are more surprising.

Can a p-value be zero?

No. A p-value can be extremely small but never exactly zero. When software such as SPSS displays .000, the value has been rounded, so report it as p < .001 instead.

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