Descriptive Statistics & Hypothesis Tests

Descriptive statistics and statistical hypothesis tests covering parametric (t-tests, ANOVA), non-parametric (Mann-Whitney, Kruskal-Wallis, Friedman), correlation, and categorical association tests.

37 procedures. Every result is computed by the open Python engine and is exportable to APA tables and reports.

Procedure	What it does	Status	Key reference
Descriptive statistics	Mean, median, variance, skewness, kurtosis, quantiles for numeric variables.	✅ Full	Virtanen et al. (2020)
Frequency distribution	Frequency tables with counts, percentages, cumulative percentages for categorical/numeric variables.	✅ Full	Virtanen et al. (2020)
One-sample t-test	Test if sample mean differs from hypothesized value; reports t-statistic, 95% CI, Cohen's d.	✅ Full	Student (1908)
Independent samples t-test	Compare means of two independent groups; includes Levene's test, optional Welch correction.	✅ Full	Student (1908); Welch (1947)
Paired t-test	Compare means of two related/paired samples; reports difference mean, SE, 95% CI, effect size.	✅ Full	Student (1908)
One-way ANOVA	Compare means across 3+ groups; includes Levene's test, Tukey HSD post-hoc, eta/omega-squared.	✅ Full	Fisher (1925); Tukey (1949)
Welch's ANOVA	Heteroscedastic one-way ANOVA without equal-variance assumption; Games-Howell post-hoc.	✅ Full	Welch (1951); Games & Howell (1976)
Two-way ANOVA	Test main effects and interaction of two factors; includes partial eta-squared effect sizes.	✅ Full	Fisher (1925)
Repeated measures ANOVA	Within-subjects ANOVA for 2+ repeated measures; Mauchly sphericity, GG/HF corrections.	✅ Full	Fisher (1925); Mauchly (1940)
Yuen's trimmed t-test	Robust two-group t-test using 20% trimmed means; insensitive to heavy tails and outliers.	✅ Full	Yuen (1974)
Mixed ANOVA	Split-plot design: between-subject factor and within-subject repeated measures.	✅ Full	Fisher (1925); Mauchly (1940)
Dunnett's test	Post-hoc test comparing each treatment group to a control group.	✅ Full	Dunnett (1955)
Cochran-Armitage test	Trend test for proportions across ordered groups.	✅ Full	Cochran (1954); Armitage (1955)
Mann-Whitney U test	Non-parametric two-group test; exact/asymptotic p-values, rank-biserial effect size.	✅ Full	Mann & Whitney (1947)
Wilcoxon signed-rank test	Non-parametric paired test; exact/asymptotic p-values, effect size r.	✅ Full	Wilcoxon (1945)
Kruskal-Wallis H test	Non-parametric 3+ group test; Dunn post-hoc with Bonferroni correction.	✅ Full	Kruskal & Wallis (1952); Dunn (1964)
Friedman test	Non-parametric repeated measures test; Kendall's W effect size.	✅ Full	Friedman (1937)
Chi-square test of independence	Association between two categorical variables; includes Cramér's V, Yates correction disclosure.	✅ Full	Pearson (1900); Campbell (2007)
Chi-square goodness-of-fit	Test if observed distribution matches expected frequencies.	✅ Full	Pearson (1900)
Fisher's exact test	Exact test for 2x2 contingency table; alternative: one/two-sided.	✅ Full	Fisher (1935); Irwin (1935)
Pearson correlation matrix	Pairwise Pearson/Spearman/Kendall correlations with p-values; listwise NA handling.	✅ Full	Pearson (1895); Spearman (1904)
Correlation (pairwise)	Single correlation with confidence interval (Fisher z-transform for Pearson).	✅ Full	Pearson (1895); Spearman (1904)
Partial correlation	Correlation between two variables controlling for others; corrected df.	✅ Full	Pearson (1895); Yule (1907)
Effect size calculator	Cohen's d/Hedges' g, eta/omega-squared, Cramér's V, Fisher's f-squared.	✅ Full	Cohen (1988)
Power analysis	Sample size / power calculation for t-test, ANOVA, correlation, chi-square, regression.	✅ Full	Cohen (1988)
Sign test	Non-parametric paired/one-sample test; binomial test on signs of differences.	✅ Full	Dixon & Mood (1946)
Runs test	Wald-Wolfowitz test for randomness; dichotomize by median/mean or threshold.	✅ Full	Wald & Wolfowitz (1940)
McNemar test	Change detection in paired binary outcomes; 2x2 table symmetry.	✅ Full	McNemar (1947)
Cochran Q test	Non-parametric repeated measures for binary outcomes (3+ measurements).	✅ Full	Cochran (1950)
Jonckheere-Terpstra test	Non-parametric alternative to ANOVA for ordered groups (monotonic trend).	✅ Full	Jonckheere (1954); Terpstra (1952)
Kendall's W	Coefficient of concordance for 2+ judges/raters across multiple items.	✅ Full	Kendall & Babington Smith (1939)
Kendall's tau	Rank correlation between two variables (tau-b for ties).	✅ Full	Kendall (1938)
Mood's median test	Non-parametric k-group test based on median; robust to outliers.	✅ Full	Mood (1954)
Permutation test	Permutation-resampling test (10000 permutations); mean difference or custom statistic.	✅ Full	Virtanen et al. (2020)
Kernel density estimate	Non-parametric density estimation; Scott/Silverman bandwidth, Gaussian kernel.	✅ Full	Virtanen et al. (2020)
MANOVA	Multivariate analysis of variance; Wilks' lambda, Pillai, Hotelling-Lawley, Roy's root.	✅ Full	Wilks (1932); Pillai (1955)
Distribution fitting + GOF	Fit Exponential-Family and related distributions (gamma, exponential, lognormal, Weibull, normal) by MLE, rank by AIC, and test fit with Kolmogorov-Smirnov. Matches R MASS::fitdistr + ks.test.	✅ Full	Massey (1951); Lilliefors (1967)