Start with the question the test asks
Suppose you want to know whether a coin is fair. You could begin with a working assumption: each flip has an equal chance of landing heads or tails. In statistical testing, this starting position is called the null hypothesis. You then collect observations and ask whether they would be unusual if that assumption and the test’s other conditions held.
A p-value answers that limited question. It is the probability, under the null hypothesis and the statistical model, of obtaining a result at least as extreme as the one observed. A small p-value means the observed result would be relatively unusual under that model. It does not, by itself, explain why the result occurred.
See the calculation in a simple example
Imagine flipping a coin 10 times and seeing nine heads. If the flips are independent and the coin is fair, how often would you expect a result this lopsided or more so? For a two-sided test, you count outcomes with nine or 10 heads and outcomes with nine or 10 tails. Together, those outcomes account for 22 of the 1,024 possible sequences of 10 flips, giving a p-value of about 0.021.
That number does not mean there is a 2.1% chance the coin is fair. The calculation began by assuming a fair coin. It tells you how often results at least this extreme would arise under that assumption. Another set of flips could look much more balanced, and the calculation also relies on conditions such as independent flips.
The phrase “at least as extreme” matters. A p-value usually considers not just the exact result you saw, but other results that the chosen test treats as equally or more inconsistent with the null hypothesis. What counts as extreme depends on the question and the test. If you had specifically asked whether the coin favors heads, a one-sided test would answer a different question from the two-sided test above.
Understand what “statistically significant” adds
Researchers often compare a p-value with a threshold called the significance level, commonly written as alpha. If they chose a threshold of 0.05 before examining the data, a p-value below 0.05 would be called statistically significant by that rule. The label means the result passed a stated decision threshold; it does not turn an uncertain finding into a fact.
The threshold is a convention, not a boundary between important and unimportant results. A p-value just above it need not be meaningfully different from one just below it. Choosing a threshold after seeing the result, or trying several analyses and reporting only the one that passes, also changes how persuasive the result is. The testing plan and the analyses attempted are part of the evidence.
Avoid three common misreadings
First, a p-value is not the probability that the null hypothesis is true. It is calculated assuming the null hypothesis and the model are true; it does not reverse that conditional statement. Deciding what to believe requires considering the study design, possible alternative explanations and other available evidence.
Second, statistical significance is not the same as practical importance. A small effect may matter little in the situation you care about, even if a large, well-measured dataset produces a small p-value. Conversely, an effect that could matter may fail to cross a significance threshold when the data are too limited to estimate it precisely.
Third, a large p-value does not prove there is no effect. It indicates that the observations are not especially unusual under the specified null model. The data may also be compatible with a range of effects, particularly when measurements are noisy or the sample is small.
Put the p-value beside the rest of the evidence
When reading a result, ask what was measured and how the observations were collected. Look for an estimate of the effect’s size, not just a test result. A confidence interval can help show which effect sizes are reasonably compatible with the data under the method used, although it should not be read as a probability that a fixed parameter lies inside that particular interval.
Then check whether the test’s assumptions fit the situation. Were observations independent where the method required independence? Were many outcomes or comparisons tested? Could missing data, selection choices or measurement problems affect the result? A p-value cannot repair a weak study design or answer a question the data did not address.
The most useful reading is therefore modest: a p-value describes how surprising the data would be under a particular set of assumptions. Treat it as one piece of a larger explanation, alongside the estimated effect, its uncertainty, the way the study was conducted and the question you actually need to answer.
