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A p-value is the probability of getting results at least as extreme as those observed, assuming the null hypothesis is true. It is not the probability the hypothesis itself is true — a smaller p-value simply signals stronger evidence against the null.
Dissertations, lab reports, and journal articles rely on p-values to justify claims. A results section that states a difference exists needs a p-value backing it up, otherwise the claim is just an opinion.
Examiners and peer reviewers check this figure closely. Getting the p-value, the test choice, and the wording of your conclusion consistent with each other is one of the most common places students lose marks.
A p-value is a number between 0 and 1 produced by a statistical test. It tells you how likely your sample data (or something more extreme) would be if there were truly no effect or no difference in the population.
Researchers use it constantly during hypothesis testing to decide whether a pattern in a dataset is likely real or could plausibly be down to random sampling variation.
The value on its own cannot tell you why an effect exists, only how unusual the observed data would be under the assumption that no effect is present in the wider population.
A test statistic — t, z, F, or chi-square, depending on the design — is calculated from your sample. This value is then compared against a known probability distribution for that test.
The p-value is the area under that distribution curve beyond your observed statistic. Software such as SPSS, R, or Excel calculates this automatically once you run the test.
Three things drive the result: the size of the difference between groups, the amount of variation in the data, and the sample size. Change any one of these and the p-value moves too.
This is why two studies with an identical effect can report very different p-values — the smaller study may simply lack the statistical power to reach significance.
Most disciplines set a significance level (α) before testing, then compare the p-value against it. The table below shows the thresholds used most often across UK academic research.
| Threshold (α) | Typical Meaning | Common Use |
|---|---|---|
| 0.10 | Weak or marginal evidence against the null | Exploratory or pilot studies |
| 0.05 | Standard cut-off for statistical significance | Most social science and business dissertations |
| 0.01 | Strong evidence against the null | Medicine, psychology, high-stakes research |
| 0.001 | Very strong evidence against the null | Genomics, physics, large-sample studies |
A p-value of 0.05 means that, if the null hypothesis were true, you would see data this extreme (or more so) about 5% of the time purely by chance.
It does not mean there is a 5% chance the null hypothesis is true, and it does not mean your finding has a 95% chance of being correct. Those are common misreadings worth avoiding in your write-up.
The 0.05 convention traces back to statistician Ronald Fisher’s work in the 1920s, where he suggested it as a practical rule of thumb rather than a universal scientific law.
Interpretation always follows the same short decision path: set your hypotheses, fix α before testing, run the test, then compare the resulting p-value with α to reach a decision.
If the p-value is at or below α, you reject the null hypothesis and describe the result as statistically significant. If it is above α, you fail to reject the null — this is not proof the null is true.
Statistical significance only tells you a result is unlikely to be random noise. It says nothing about whether the effect is large enough to matter practically, clinically, or commercially.
With a very large sample, even a tiny, trivial difference can produce a low p-value. Always report an effect size alongside the p-value so readers can judge real-world importance.
Sample size has an outsized influence on p-values. A modest, genuine effect can stay non-significant in a small sample simply because there is not enough data to detect it reliably.
Conversely, in a survey of several thousand respondents, a near-meaningless one-point difference on a rating scale can return p < .001. The p-value reflects certainty about an effect existing, not its size.
Before collecting data, a power analysis helps estimate the sample size needed to detect a realistic effect. This is often expected in a dissertation methodology chapter.
The logic of a p-value stays the same across tests, but the statistic feeding into it changes depending on your data and research question.
| Test | Compares | Reported Alongside p |
|---|---|---|
| Independent t-test | Means of two separate groups | t value, degrees of freedom |
| Paired t-test | Means of the same group, two time points | t value, degrees of freedom |
| ANOVA | Means across three or more groups | F value, both degrees of freedom |
| Chi-square | Association between categorical variables | Chi-square value, degrees of freedom |
| Correlation (Pearson/Spearman) | Strength of a relationship between variables | r or rho value, sample size |
Choosing the correct test depends on your data type and design, which is why checking test assumptions matters before you even look at the resulting p-value.
A few misunderstandings appear repeatedly in student write-ups and even published papers. Being clear on these strengthens your results and discussion sections considerably.
Most UK social science departments expect APA-style reporting: italicised statistic, degrees of freedom in brackets, then the exact p-value to two or three decimal places.
Write “p = .019” rather than “p = 0.019” (no leading zero in APA), and switch to “p < .001” once the exact value rounds to zero. Never write “p = 0.000”.
Keep wording consistent: “significant” only for results at or below α, “non-significant” or “not significant” for results above it — avoid words like “close to significant”.
A one-tailed test places all of α in a single direction and is used when you predict an effect will go one specific way, such as “scores will increase”.
A two-tailed test splits α across both directions and is the safer default, since it detects a difference regardless of which way it points. Most dissertation supervisors expect two-tailed testing unless a strong directional case is made.
The p-value is only one step inside a wider process. Before running any test, you need a clearly stated null hypothesis and its alternative.
You also need to check the assumptions for hypothesis testing — such as normality and equal variances — before trusting any p-value the test produces.
For more worked walkthroughs on choosing tests and interpreting output, browse our full statistical analysis guide hub for further examples.
Choosing the right test, checking assumptions, and writing up p-values correctly can be time-consuming when a dissertation deadline is close. Support is available if you want a second opinion on your results chapter.
Our statistical analysis service covers test selection, SPSS output interpretation, and results write-ups, and our SPSS data analysis help is available for individual chapters or full projects.
If you also need support drafting the surrounding chapters, our dissertation writing service can help structure the whole piece around your findings.
A p-value is the probability of seeing results as extreme as yours, or more extreme, if the null hypothesis were actually true. A small p-value means your data would be unusual under the null hypothesis, giving evidence against it. It is not the probability your finding is correct.
A p-value of 0.05 means there is a 5% chance of observing data this extreme if the null hypothesis were true. Researchers commonly treat 0.05 as the cut-off for statistical significance, though it remains a convention rather than a strict scientific rule.
A p-value measures how compatible your sample data are with the null hypothesis, not how large or important an effect is. It combines both the size of the difference and the sample size, so a tiny effect can still produce a low p-value in large datasets.
A lower p-value gives stronger evidence against the null hypothesis, but it does not automatically mean the effect is meaningful. A very low p-value from a huge sample can still describe a trivial, practically unimportant difference, so effect size should always be reported alongside it.
A p-value is a specific number produced by a test; statistical significance is the label applied when that p-value falls at or below your chosen threshold, usually 0.05. Significance confirms a result is unlikely to be random chance, not that it is practically important.
No. A high p-value only means there was not enough evidence to reject the null hypothesis in this particular sample. It never proves the null hypothesis is true, since a non-significant result can also result from a small sample or a weak test design.
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