What Does Statistically Significant Mean? P-Values Explained

A result is statistically significant when it would be unlikely to appear by chance alone if there were really no effect. The cutoff is chosen before data collection, and the most common one is a p-value below 0.05. Statistical significance says nothing about whether a finding is large, important or true.

The phrase appears in reports on drug trials, diet research and psychology experiments, often treated as a stamp of approval. Its meaning is much narrower, and knowing what it covers makes research easier to read accurately.

What is a p-value?

A p-value is the probability of getting results at least as extreme as the ones observed, assuming the “null hypothesis” is true. The null hypothesis is the dull default: the treatment does nothing, the two groups do not differ, there is no link between the two things measured.

Suppose a researcher tries a new fertilizer on plants and the treated plants grow taller. A p-value of 0.03 means that if the fertilizer truly had no effect, random variation alone would produce a difference this large or larger about 3 times in 100. That is rare enough, by convention, to count as evidence against “no effect.”

Why is 0.05 the usual cutoff?

The 0.05 threshold is a convention. It became popular in the early 20th century and stuck because it is simple and easy to agree on. A researcher picks it in advance as the significance level, often written as alpha.

Some fields use stricter cutoffs. Particle physics demands far smaller probabilities before anyone claims a discovery, while early exploratory work sometimes accepts a looser one. A result with p = 0.049 is barely different from one with p = 0.051, even though only the first clears the bar.

Does statistically significant mean important?

No. Significance depends on sample size as well as effect size. With thousands of participants, even a tiny difference can produce a very small p-value. A blood pressure drug that lowers pressure by a barely measurable amount can be statistically significant in a huge trial and still make no practical difference to patients.

The reverse happens too. A small trial of a treatment that really works may miss significance because it had too few participants to detect the effect. A “not significant” result means the data could not rule out chance at the chosen threshold. It does not prove that nothing is going on.

To judge size, look for the effect size and the confidence interval. A confidence interval is a range of values consistent with the data. A narrow range far from zero points to a clear effect, while a wide range that includes zero leaves the result uncertain.

What does a p-value leave out?

A p-value does not give the probability that the hypothesis is true. A p-value of 0.04 does not mean there is a 96 percent chance the finding is real. It only describes how surprising the data would be if the null hypothesis were correct.

It also says nothing about quality. A badly designed experiment, a biased sample or faulty measurements can all produce small p-values. Observational studies, which watch what people already do rather than assigning a treatment, can produce significant links that come from a third factor instead of cause and effect.

How do researchers end up with misleading significant results?

The main cause is running many tests. If you test 20 unrelated things at the 0.05 level, about one should look significant by chance alone. Reporting only that one result, sometimes called p-hacking, makes noise look like a discovery.

Other causes include stopping a trial as soon as the numbers look good, trying several ways of analyzing the same data and publishing only positive results. Careful researchers counter these by pre-registering the plan before collecting data, adjusting for multiple comparisons and repeating the work with new participants. A single surprising result is therefore a starting point, and replication by independent teams is what builds confidence.

The same caution applies across science. Claims about what sleep science does and does not know and about common food and sleep beliefs such as turkey and tryptophan are good examples of topics where one headline result rarely settles the question.

How can you read a significant result sensibly?

1. Find the effect size, not just the p-value. Ask how big the difference is in real units.
2. Check the sample size. Very small and very large samples both need extra care.
3. Look at the confidence interval for the range of plausible values.
4. Ask whether it was an experiment with random assignment or an observational comparison.
5. Check whether independent teams have reached the same result.

For a plain reference on the methods behind these tests, the NIST/SEMATECH e-Handbook of Statistical Methods is a free resource from a US government laboratory.

Quick answers

What p-value is considered statistically significant?

Most research uses p below 0.05, meaning a result that would occur less than 5 percent of the time by chance if there were no real effect. Some fields set a stricter threshold, and the cutoff should be chosen before the data are collected.

Can a result be significant but not meaningful?

Yes. A large sample can detect a very small difference that has no practical value. That is why effect size matters as much as the p-value.

What does “not statistically significant” mean?

The data did not provide enough evidence to rule out chance at the chosen level. Because a small or underpowered trial can miss a real effect, it is not proof of no effect.

Is p less than 0.05 the same as proof?

No. A single significant result is evidence, not proof. Confidence grows when different teams repeat the work and get consistent results.