A p-value measures how unusual a study’s observed result would be under a specified statistical model, often one that assumes no effect. It does not tell you the probability that the hypothesis is true, that chance alone caused the result, or that an effect matters in practice. To interpret a finding, consider the study design, estimated effect, uncertainty, and analysis choices—not just whether the p-value is below 0.05.
What a p-value means
The American Statistical Association defines a p-value, informally, as “the probability under a specified statistical model that a statistical summary of the data (e.g., the sample mean difference between two compared groups) would be equal to or more extreme than its observed value.” The definition is conditional: it starts by assuming a model and asks how the observed data summary compares with what that model predicts.
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For example, if a study reports p = 0.03, then—assuming the test’s model and null hypothesis, and the assumptions used to calculate the value—a result at least as extreme as the observed one would occur with probability 0.03 under the test procedure. This does not mean there is a 3% chance the null hypothesis is true, or a 97% chance the finding is real. The p-value assigns a probability to data summaries under a model, not to the truth of a hypothesis.
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1Clear out junk files and repair common Windows errors2Scan for outdated or missing drivers - takes under a minute3Repair Windows errors before they cause bigger problemsA smaller p-value indicates greater incompatibility between the observed data and the specified model, if the assumptions hold. It is a limited statement about compatibility, not a verdict on whether a claim is true. The ASA’s 2016 statement on p-values and its accompanying explanation stress that interpretation depends on context and other evidence.
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What does p < 0.05 mean?
In some analyses, 0.05 is a decision threshold chosen in advance. A result below it is often called “statistically significant” under that rule. The label describes the outcome of applying the rule; it does not certify that a result is true, important, or worth acting on.
Values just above and below the cutoff are not categorically different kinds of evidence. A p-value of 0.049 and one of 0.051 should not be treated as a sharp divide between a real effect and no effect. If a study needs a yes-or-no decision, readers should look for the rule used and the reason for choosing it, while keeping the underlying estimate and uncertainty in view. The ASA cautions against basing scientific, business, or policy conclusions only on whether a p-value crosses a fixed threshold.
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What a p-value cannot tell you
- Whether the null hypothesis is true. The p-value is calculated under a specified model, often one that includes the null hypothesis; it is not the probability that the null is true.
- Whether chance alone caused the result. It describes how data summaries compare with a model, not the cause of the observed data.
- How large or important the effect is. A small effect can yield a small p-value in a large or precise study. A substantial effect can yield a larger p-value in a small or imprecise study. The ASA states that “a p-value, or statistical significance, does not measure the size of an effect or the importance of a result.”
- That there is no effect when the p-value is large. A large value does not prove the null hypothesis or establish the alternative; it indicates that the observed result is not especially incompatible with the specified model under the test assumptions.
- A complete measure of evidence. A p-value alone leaves out design quality, measurement, assumptions, effect size, uncertainty, and relevant outside evidence.
What to examine alongside the p-value
Start with the estimated effect: what changed, by how much, and in which direction? Then examine an uncertainty measure, such as a confidence interval, and ask whether the range includes effects that would matter in the real setting. An interval gives more information about plausible effect sizes than a significance label alone, though it too must be interpreted in light of the study and its assumptions.
Next, assess how the evidence was produced. Consider whether the study design can answer the question, whether outcomes were measured well, whether the model assumptions are plausible, and whether other evidence points in the same direction. When comparing studies, consider these factors as well as the number of analyses or outcomes examined. A lower p-value by itself does not mean a larger effect or a more important finding.
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Why multiple analyses and selective reporting matter
Researchers may test many hypotheses, examine several outcomes, or make multiple analytic choices. If only the analyses with small p-values are reported, readers cannot interpret those values as though the reported test were the only one considered. The path from data to reported result matters: what hypotheses were explored, what data-collection decisions were made, which analyses were conducted, and which p-values were calculated?
Transparent reporting of those choices helps readers judge the result. There is no single correction that fits every multiple-testing problem; an appropriate approach depends on the analysis and research goal. Selective presentation, however, can undermine interpretation when readers cannot see what was tried.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Are there alternatives to p-values?
No one method is the right replacement for every question. Depending on the goal and assumptions, researchers may use estimation approaches such as confidence, credibility, or prediction intervals; Bayesian methods; likelihood ratios or Bayes factors; decision-theoretic models; or false discovery rates. These approaches answer different questions and are not magic substitutes for careful design and interpretation.
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