P-value (Probability Value)

P-value (Probability Value): The p-value is a statistical measure used in research to help decide whether the results of a study are likely due to chance. More specifically, it represents the probability of observing results as extreme, or more extreme, than those found in the study, assuming the null hypothesis is true

Remember, the null hypothesis is the hypothesis of "no effect." A small or very small p-value (approaching 0.0) suggests that the observed results would be highly unlikely if the null hypothesis were true and there was truly no effect. A very small probability of no effect (typically less than 0.05) leads researchers to reject the null hypothesis.

Informal definition: “The p-value is the degree to which the null (no effect) hypothesis is embarrassed by the data.”

Related Terms

Systematic Review
Evidence-based practice
Levels of evidence
Meta-analysis
P-value
Null Hypothesis
Vote-Counting
Regression to the Mean

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Purpose and Function

P-values are used in hypothesis testing to evaluate whether study results are statistically significant. A common threshold for significance is p < 0.05, meaning there is less than a 5% probability of observing the study’s results, or more extreme results, assuming the null hypothesis is true. In such cases, researchers may reject the null hypothesis and consider the findings statistically significant.

However, this does not mean there is a 5% chance the null hypothesis is true (this is a common misinterpretation). The p-value is a conditional probability: it tells us the likelihood of the observed data given that the null hypothesis is true, not the probability that the hypothesis itself is true.

For example, a p-value of 0.05 means that, if the null hypothesis were correct, we would expect to observe similar or more extreme results in roughly 5 out of every 100 repeated studies. This does not confirm an effect; however, it suggests that the results are unusual enough under the null hypothesis to warrant its rejection.

What a P-value Is Not

Not the probability that the hypothesis is true or false
Not a direct measure of the effect’s size or importance
Not a guarantee that the results are replicable
Not a statement about clinical relevance

Statistical Significance

Rejecting the null hypothesis (e.g., p < 0.05) does not prove that a specific alternative hypothesis is correct, unless only one plausible alternative exists. It simply indicates that either:

A real effect is present
A rare event occurred under the assumption of no effect

Applied Example

Statement from a study: “There were statistically significant differences between the intervention and control groups (p < 0.05).”

Correct Interpretation: If we started with the assumption that no true difference exists, the chance of observing results this extreme, or more extreme, is less than 5%. That is, if the null (no effect) hypothesis were true, and the study were repeated 100 times, we would expect to see results like this fewer than 5 times in 100 repetitions.

Poor Interpretation: “The intervention works and should be recommended for all cases.”
Better Interpretation: “Assuming no true effect, there is less than a 5% probability of observing results as extreme as those found in this study. Because this is considered an unlikely outcome, the null hypothesis is rejected. This suggests that an effect may have occurred under the conditions tested, but further research is needed to confirm the finding and assess its generalizability.”

Frequently Asked Questions (FAQs)

What does the "P" in P-value stand for?

In the context of statistics, the "p" in p-value stands for probability

What does “p < 0.05” really mean?

It means that, assuming the null hypothesis is true, there is less than a 5% chance of observing the result seen in the study (or a more extreme result). Generally, this is considered sufficient evidence to reject the null hypothesis and consider the likelihood of an effect better supported.

Is a value of p < 0.05 or p < 0.01 "better"?

A p-value < 0.05 corresponds to a 95% confidence level, while a p-value < 0.01 corresponds to a 99% confidence level. The lower the p-value, the smaller the probability that the observed result occurred due to random chance (assuming the null hypothesis is true). Thus, a p-value < 0.01 provides stronger statistical evidence against the null hypothesis than p < 0.05. This may be considered stronger evidence that an effect occurred, and that we can refute the null without additional evidence to contradict this assertion.

Is the p-value the probability that the null hypothesis is true?

No. The p-value assumes the null hypothesis is true. It evaluates the probability of the data, not the hypothesis.

Can a statistically significant result be clinically meaningless?

Yes. P-values do not indicate the size or importance of an effect: statistical significance ≠ and practical significance. In fact, it is not hard to imagine scenarios in which a small chance of an effect may be worth the risk, and a higher p-value may be accepted. For example, consider a cancer drug that cured several people in a study with a small participant pool, such that the effect size did not reach statistical significance at p < 0.05. Do you continue to offer the drug to additional patients?

What if a study fails to reach p < 0.05?

Based on current standards, it implies that the data did not provide sufficient evidence to reject the null hypothesis. It does not confirm that the null is true or that the intervention is ineffective. In fact, it can be argued that p < 0.05 is a rather arbitrary benchmark. Depending on the scenario, this benchmark may be too conservative or not conservative enough.

Brookbush Institute Pointers on P-values

P-values assume the null is true: P-values do not tell us whether the hypothesis is true; they tell us how surprising the observed data are if the null were true.
P < 0.05 is not a magic cutoff: A p-value of 0.049 is not meaningfully different from 0.051. Significance should be interpreted within the broader context of study design, sample size, effect size, and prior evidence.
The p-value is a measure of surprise, not truth: Low p-values indicate that the observed result is unlikely under the null hypothesis, but not impossible. Outliers are expected in probabilistic systems.
Easily distorted by sample size: In large studies, very small effects can appear statistically significant. In small studies, meaningful effects may not reach statistical significance. P-values must always be interpreted in relation to sample size and variance.
Does not account for effect size, clinical relevance, or study quality: A small p-value does not indicate a meaningful effect, nor does it compensate for poor methodology or an underpowered design. Statistical significance should always be considered in conjunction with effect magnitude, relevance, and practical applicability.
False conclusions can arise from poor interpretation: Interpreting “failure to reject the null” as proof of ineffectiveness is erroneous, especially in underpowered studies. Likewise, interpreting “statistical significance” as proof of clinical value is equally misleading.
Patterns matter more than single studies: A single p-value may mislead. A pattern of consistently significant findings across multiple high-quality studies is a far stronger indicator of a true effect.

P-value (Probability Value)