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How we check accuracy
Every calculator is tested against established statistical software on several test datasets. In the current release, 375 checks across 19 procedures (including Tukey HSD, the Dunn post hoc test and repeated measures ANOVA with sphericity corrections) matched the reference values from Python scipy, statsmodels and pingouin to within 0.0001, and in nearly all cases to eight or more decimal places.
| Calculator | Reference used for validation |
|---|---|
| Cronbach’s alpha | pingouin.cronbach_alpha; Feldt CI |
| Sample size | Cochran and Yamane formulas |
| Independent t test | scipy ttest_ind (Student and Welch), Levene’s test |
| Paired t test | scipy ttest_rel |
| One-way ANOVA + Tukey HSD | scipy f_oneway; statsmodels pairwise_tukeyhsd; pingouin |
| Pearson correlation | scipy pearsonr with confidence interval |
| Chi-square | scipy chi2_contingency (no continuity correction) |
| Cohen’s d | pingouin effect size conversion |
| Power analysis | statsmodels TTestIndPower |
| Descriptive statistics | numpy and scipy (bias-corrected skewness and kurtosis) |
| Mann-Whitney U | scipy mannwhitneyu (asymptotic, tie-corrected) |
| Wilcoxon signed-rank | scipy wilcoxon (zero_method=wilcox) |
| Kruskal-Wallis + Dunn | scipy kruskal; scikit-posthocs posthoc_dunn (Bonferroni) |
| Spearman correlation | scipy spearmanr |
| Linear regression | statsmodels OLS and variance_inflation_factor |
| Cohen’s kappa | statsmodels cohens_kappa |
| Repeated measures ANOVA | pingouin rm_anova, sphericity (Mauchly), epsilon (GG, HF) and pairwise_tests (Bonferroni) |
References
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
- Cochran, W. G. (1977). Sampling techniques (3rd ed.). Wiley.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.
- Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174.
- Girden, E. R. (1992). ANOVA: Repeated measures. SAGE.
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE.
- Yamane, T. (1967). Statistics: An introductory analysis (2nd ed.). Harper & Row.
Written and maintained by the ScholarCalc team. Last reviewed: November 2026.