Examples

This gallery walks through every public feature of mathematicskit.statistics: descriptive statistics, hypothesis tests, confidence intervals, ordinary least-squares regression, correlation, maximum likelihood, nonparametric tests, bootstrap and jackknife resampling, shrinkage estimation, and multiple-testing corrections.

See also the narrative tutorial:

• Randomness, Three Ways

Each script in this gallery is self-contained and can be run directly with python examples/statistics/<section>/<script>.py.

Sections

• descriptive – the five-number summary, skewness, and kurtosis, and Gauss’s normal law of measurement errors.

• hypothesis_tests – z-tests, t-tests, chi-square tests, ANOVA, and Fisher’s exact test.

• confidence_intervals – intervals for means, proportions, and variances.

• regression – ordinary least squares with residual diagnostics.

• correlation – Pearson’s and Spearman’s correlation coefficients.

• likelihood – maximum-likelihood fitting and Wilks’s likelihood-ratio test.

• nonparametric – the Kolmogorov-Smirnov, Wilcoxon signed-rank, and Mann-Whitney U tests.

• bootstrap – bootstrap confidence intervals via scipy.stats.bootstrap, and the jackknife.

• shrinkage – the James-Stein estimator.

• multiple_testing – Bonferroni and Benjamini-Hochberg corrections.

Bootstrap resampling

Bootstrap confidence intervals via scipy.stats.bootstrap, and the leave-one-out jackknife.

Bootstrap vs. parametric confidence intervals

Bootstrap vs. parametric confidence intervals

The jackknife

The jackknife

Confidence intervals

Intervals for means, proportions, and variances.

Confirming a 95% confidence interval’s coverage by simulation

Confirming a 95% confidence interval's coverage by simulation

Correlation

Pearson’s product-moment and Spearman’s rank correlation coefficients.

Galton’s heights and Pearson’s correlation

Galton's heights and Pearson's correlation

Spearman’s rank correlation

Spearman's rank correlation

Descriptive statistics

The five-number summary, skewness, and kurtosis, and Gauss’s normal law of measurement errors.

Descriptive statistics and the five-number summary

Descriptive statistics and the five-number summary

Gauss’s normal law of errors

Gauss's normal law of errors

Hypothesis tests

z-tests, Student’s t-tests, chi-square tests (goodness-of-fit and independence), Fisher’s exact test, and one-way ANOVA.

Student’s t-distribution and the small-sample t-test

Student's t-distribution and the small-sample t-test

Chi-square goodness-of-fit and independence tests

Chi-square goodness-of-fit and independence tests

Fisher’s exact test and the lady tasting tea

Fisher's exact test and the lady tasting tea

Fisher’s one-way analysis of variance

Fisher's one-way analysis of variance

Likelihood

Maximum-likelihood fitting and the likelihood-ratio test.

Fisher’s maximum likelihood

Fisher's maximum likelihood

Wilks’s theorem and the likelihood-ratio test

Wilks's theorem and the likelihood-ratio test

Multiple testing

Bonferroni and Benjamini-Hochberg corrections for many simultaneous tests.

Benjamini-Hochberg and the false discovery rate

Benjamini-Hochberg and the false discovery rate

Nonparametric tests

The Kolmogorov-Smirnov test and the Wilcoxon and Mann-Whitney rank tests.

The Kolmogorov-Smirnov test

The Kolmogorov-Smirnov test

Wilcoxon and Mann-Whitney rank tests

Wilcoxon and Mann-Whitney rank tests

Linear regression

Ordinary least squares with residual diagnostics.

OLS regression with residual diagnostics

OLS regression with residual diagnostics

Shrinkage estimation

The James-Stein estimator and Stein’s paradox.

Stein’s paradox

Stein's paradox