In statistical hypothesis testing, the p-value is the probability of obtaining results at least as extreme as the observed results, given that the null hypothesis is true. It is a key concept used to determine the statistical significance of findings.


The p-value is often used as a threshold for rejecting the null hypothesis:

  • Large p-values (e.g., p-value > 0.05) suggest weak evidence against the null hypothesis. This means the observed data could likely have occurred simply due to chance variation.
  • Small p-values (e.g., p-value ≤ 0.05) offer stronger evidence against the null hypothesis, implying the observed results are unlikely to have happened by chance alone.

The 0.05 significance level is a common but arbitrary threshold. It's crucial to consider the context of the study and interpret p-values in conjunction with other factors like effect sizes and potential confounding variables.


Calculating a p-value involves the following:

  1. Null Hypothesis and Test Statistic: Define the null hypothesis (H₀) and choose an appropriate test statistic based on the data and the hypothesis you're testing.
  2. Distribution: Determine the sampling distribution of the test statistic under the assumption that the null hypothesis is true.
  3. Calculation: Calculate the probability of obtaining a test statistic as extreme or more extreme than the one observed from your data, within the assumed sampling distribution. This probability is the p-value.

Misconceptions and Limitations

Important considerations about p-values:

  • Not a Measure of Hypothesis Truth: The p-value does not indicate the probability that the null hypothesis is true, nor the likelihood that the alternative hypothesis is true.
  • No Guarantee of Practical Significance: Statistical significance (a small p-value) does not necessarily mean the observed effect has practical importance.
  • Sensitivity to Sample Size: With very large sample sizes, even small and practically meaningless differences may become statistically significant.
  • Potential for Misinterpretation: P-values are often misinterpreted and overemphasized. It's important to use them as one piece of evidence within a broader research context.

Alternatives and Best Practices

Statistical practitioners increasingly advocate for:

  • Reporting Effect Sizes: Focus on practical significance by reporting effect sizes alongside p-values.
  • Confidence Intervals: Provide confidence intervals that offer a range of plausible values for the true population parameter.
  • Bayesian Techniques: When feasible, consider Bayesian approaches to hypothesis testing, which yield more direct probabilities about the hypotheses under investigation.