P-Value (probability value)#
The probability of data at least as extreme as observed, assuming the null is true.
Important
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What it is#
The p-value is the probability of observing data at least as extreme as what you saw, assuming the null hypothesis \(H_0\) is true. It is a measure of evidence against \(H_0\): a low p-value means the data would be surprising under \(H_0\) (stronger evidence against it), a high one means the data sit comfortably with \(H_0\).
Reading it#
By convention \(p < 0.01\) is very strong evidence, \(p < 0.05\) is “significant”, \(p < 0.10\) is weak, and \(p > 0.10\) is not significant. The decision rule pairs it with a threshold: if \(p \le \alpha\), reject \(H_0\); if \(p > \alpha\), fail to reject.
How it’s computed#
Form the test statistic (z, t, \(\chi^2\)…) and find the tail probability of a value that extreme under its distribution — one tail for a one-sided test, both for two-sided. For a two-tailed t-test,
For example, 17 heads in 20 tosses gives a binomial p of about 0.003 against a fair coin (reject); a two-sample test with \(t = 2.1, df = 28\) gives \(p \approx 0.045\) (reject at 0.05).
What it is not#
Three persistent misconceptions: the p-value is not the probability that \(H_0\) is true; it is not an effect size (a tiny p means surprising, not large); and it is sample-size sensitive — huge samples make trivial effects significant, tiny samples can miss real ones. Always read it alongside an effect size and a confidence interval.
Theme: Statistical Inference & Power · All terminology
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Mind map — connected ideas
Statistical Significance · Significance Level (α) · Hypothesis Testing · Type I Error · Effect Size (δ) · Z-Test
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More in Statistical Inference & Power
A Priori Power Analysis · Chi-square (χ²) Test · Clopper–Pearson Interval · Compromise Power Analysis · Confidence Intervals (CIs) · Effect Size (δ) · Hypothesis Testing · Kolmogorov–Smirnov (KS) Test · Minimum Detectable Lift (MDL) · Post Hoc Power Analysis · Power (1 – β) · Power Analysis · Sample size · Significance Level (α)
See also
Source article Adapted (context, re-expressed) in our own words from: P-Value (probability value) (insightful-data-lab.com).