P-Values

Statistics · Axiom Academy

Learn what p-values really mean, how to interpret them correctly, and avoid common statistical pitfalls The p-value answers this specific question: "If there were truly no effect (if H₀ were true), how likely would we be to see data like what we observed, or even more extreme?" Null Hypothesis (H₀): The assumption of "no effect" or "no difference" Test Statistic: A value calculated from sample data (e.g., z-score, t-statistic) P-value: The area under the probability distribution curve beyond the test statistic 2. Correct Interpretation of P-Values Understanding what p-values tell us—and what they don't—is critical for proper statistical reasoning. A measure of compatibility between your data and the null hypothesis The probability of the data (or more extreme) given H₀ is true A continuous measure of evidence against H₀ The p-value is NOT the probability that H₀ is true The p-value is NOT the probability that the results occurred by chance The p-value is NOT the probability that you made a mistake 1 - p is NOT the probability that the alternative hypothesis is true A non-significant p-value does NOT prove the null hypothesis A one-tailed test is used when we have a directional hypothesis—we're only interested in deviations in one specific direction. Examples of one-tailed hypotheses: H₁: μ > μ₀ (right-tailed: testing if mean is greater) H₁: μ < μ₀ (left-tailed: testing if mean is smaller)

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