Free Statistical Analysis Online Calculators, Guides and Ethical Support
Resources
Practical guides for SPSS, R, Python, Excel, Power BI, statistical tests, calculators, dashboards and interpretation.
Choosing between a two-sample t test and a paired t test is a design decision before it is a calculation. Independent groups require a two-sample procedure; matched people, repeated measurements, or deliberately paired units require a one-sample t test on the within-pair differences.
The chi square goodness of fit test compares one categorical variable’s observed counts with a fully specified distribution of expected proportions. College Board removed this procedure from the revised AP Statistics course beginning in 2026–27, so this page is retained for older released material, enrichment, and college-statistics continuity.
Chi-square tests of homogeneity and independence use the same expected-count formula and chi-square statistic but begin from different data-collection stories. Homogeneity compares categorical distributions across populations or treatments; independence asks whether two categorical variables are associated within one population.
Chi-square calculator with expected counts, df, critical values, p-value logic, worked cases, MCQs, FRQs, and a 20-method statistics engine.
Legacy regression-slope inference guide for older AP/college materials, with worked cases, t procedures, interpretation, and current-course status.
Chi-square assumptions and expected-count diagnostics with design checks, 20 cases, focused MCQs, FRQs, and interpretation guidance.
36 visible MCQs, 14 FRQ sets, formulas, worked answers, and direct links to the complete AP Statistics practice system.
Exact one-sample inference for a binary proportion Binomial Test: Formula, Calculator, Example, Python, R, SPSS and Excel Guide Binomial Test is an exact hypothesis test for…
Unconditional exact inference for two independent proportions Barnard’s Exact Test: Formula, Calculator, Interpretation, Python, R, SPSS, SAS and Excel Guide Barnard’s Exact Test is an unconditional…
A verified 649-case regression assumptions audit covering functional form, residual normality, variance, independence, VIF, influence, and matched Python, R, SPSS, and Excel evidence.