P-value
A p-value is the probability, assuming a specified null hypothesis, of obtaining a test statistic or result at least as extreme as the observed one.
Statistics Slam Dunk
A p-value is the probability, under a specified null hypothesis, of obtaining a result at least as extreme as the observed result according to a test statistic.
- How it is used
- Supports null-hypothesis decisions in normality tests, t-tests, correlation tests, ANOVAs, and regression modeling.
- How deep it goes
- Defines threshold-based interpretation and demonstrates it across R test outputs, without deriving p-value calculations.
- Examples
- Uses NBA foul calls, free-throw attempts, salary and win-share Gini coefficients, normality checks, and wins models.
- What you can do after
- Apply it via base R tests and model summaries to reject or fail to reject a stated null hypothesis.
Statistics Every Programmer Needs
A p-value is the probability, under a specified null hypothesis, of obtaining a result at least as extreme as the observed result.
- How it is used
- Guides null-hypothesis decisions about regression models, individual predictors, and observed-versus-expected counts.
- How deep it goes
- Defines the conditional probability, works through threshold decisions, and demonstrates a chi-square computation without deriving a general p-value formula.
- Examples
- Uses runner-time regression, raisin-variety classification, and a SciPy test of world-population leading digits against Benford’s law.
- What you can do after
- Apply it via SciPy and statsmodels to interpret significance while checking fit, assumptions, and predictive performance separately.
Read how Statistics Every Programmer Needs explains p-value →
Grokking Statistics
A p-value is a probability, calculated under the null hypothesis, of obtaining a result at least as extreme as the observed result.
- How it is used
- Uses p-values to judge whether sample evidence challenges a null hypothesis in mean and correlation tests.
- How deep it goes
- Defines tail-area meaning, contrasts one- and two-tailed calculations, and applies decision rules without deriving proofs.
- Examples
- Uses tea identification, potato chip weights, and sports drink sales versus temperature datasets.
- What you can do after
- Apply it via SciPy to calculate p-values and decide whether to reject a specified null hypothesis.
Effective Data Analysis
A p-value is the probability of obtaining a test statistic at least as extreme as the observed value assuming the null hypothesis is true.
- How it is used
- Uses p-values to assess statistical significance when interpreting test results and communicating group comparisons.
- How deep it goes
- Defines the interpretation and works through thresholds, sample size, and test results without deriving p-value calculations.
- Examples
- Uses a t-distribution table, a simulated independent-samples t-test, and Kruskal–Wallis post hoc comparisons.
- What you can do after
- Practice/perform sample-size planning with statsmodels and independent-samples t-tests with SciPy, then compare results against chosen alpha levels.
Causal AI
A p-value is the probability, under a null hypothesis, of obtaining a test statistic at least as extreme as the observed one.
- How it is used
- Uses p-values to assess statistical evidence for dependence or conditional independence while building and checking causal models.
- How deep it goes
- Explains the definition, threshold rule, bootstrap workflow, and sample-size limitation, but stops short of deriving test statistics.
- Examples
- Uses E ⊥ T | O, R, a 30-point dataset, bootstrap resampling, confidence intervals, and plots of p-values against data size.
- What you can do after
- Diagnose/debug conditional-independence tests by comparing thresholds, bootstrapping across sample sizes, and interpreting results cautiously.
Related concepts
- correlation testingproduced by · Correlation testing is a statistical procedure for evaluating the association between variables, often against a specified null value.
- Shapiro–Wilk testproduced by · The Shapiro–Wilk test is a statistical hypothesis test assessing whether a sample is consistent with a normal distribution.
- null hypothesismeasures · A null hypothesis is a designated baseline statistical claim, typically asserting that an effect, difference, or association is absent.
- hypothesis testingused by · Hypothesis testing is a formal statistical procedure that uses observed data to evaluate evidence about a specified hypothesis, often a null hypothesis.
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