Statistical Accuracy Verification
Our checks compare selected numerical outputs with independent R and SciPy references, test invalid and boundary inputs, and exercise calculator behavior in a browser. Passing these checks provides evidence for the cases tested, not a guarantee for every dataset.
Verification Summary
Recorded audit verification: development commit 2dbd051, 19 September 2026.
These are different kinds of evidence and should not be added together as one test count. The independent comparisons cover 41 calculation modules and reported no mismatches in this run.
Our Verification Methodology
Selected statistics, probabilities and confidence intervals are compared with independently generated reference values from R and SciPy. The fixtures identify the commands or formulas, reference versions, tail conventions and tolerances used. Some calculations use documented approximations, which may differ from exact tests.
Boundary and browser regressions complement the numerical checks. The repository includes a verification workflow for pushes and pull requests; its latest run establishes whether those checks passed for a particular revision. An untested output or a documented fixture exclusion should not be treated as independently verified.
Methods Covered by Automated Checks
The methods below have automated calculation or regression coverage. The depth of coverage varies by method. A check mark does not mean that every output, assumption or possible dataset has been independently verified. Independent R and SciPy comparisons apply only to the recorded fixtures and generated cases.
Parametric Tests
- ✓ Independent Samples T-Test
- ✓ Paired Samples T-Test
- ✓ One-Sample T-Test
- ✓ Z-Test for Sample Mean
- ✓ One-Way ANOVA
- ✓ Two-Way ANOVA
- ✓ Repeated Measures ANOVA
- ✓ Tukey HSD Post-Hoc Test
- ✓ Levene's Test
Non-Parametric Tests
- ✓ Mann-Whitney U Test
- ✓ Wilcoxon Signed-Rank Test
- ✓ Kruskal-Wallis Test
- ✓ Friedman Test
- ✓ Sign Test
- ✓ Kolmogorov-Smirnov Test
Correlation & Regression
- ✓ Pearson Correlation
- ✓ Spearman Rank Correlation
- ✓ Kendall's Tau
- ✓ Point-Biserial Correlation
- ✓ Simple Linear Regression
- ✓ Multiple Regression
- ✓ Standard Error of Estimate
Categorical Data Analysis
- ✓ Chi-Square Test (2×2)
- ✓ Chi-Square Test (N×M)
- ✓ Chi-Square Goodness of Fit
- ✓ Fisher's Exact Test
- ✓ Binomial Test
- ✓ Phi Coefficient
- ✓ Cohen's Kappa
Effect Sizes & Confidence Intervals
- ✓ Cohen's d
- ✓ Risk Ratio & Odds Ratio
- ✓ Number Needed to Treat
- ✓ Confidence Intervals (t-based)
- ✓ Confidence Intervals (z-based)
- ✓ CI for Difference of Means
Utility Calculations
- ✓ Descriptive Statistics
- ✓ Z-Scores & Percentiles
- ✓ Standard Error
- ✓ Sample Size Calculator
- ✓ Skewness & Kurtosis
- ✓ Bayes' Theorem
- ✓ Coefficient of Variation
- ✓ Interquartile Range (IQR)
- ✓ Frequency Distribution
Outlier Detection
- ✓ Grubbs Test
- ✓ Generalized ESD Test
P-Values & Critical Values
- ✓ Z (Normal) Distribution
- ✓ T Distribution
- ✓ Chi-Square Distribution
- ✓ F Distribution
- ✓ Power Analysis (t-test)
- ✓ Power Analysis (ANOVA)
What the Evidence Shows
| Evidence | Recorded result (19 September 2026) | What it does not establish |
|---|---|---|
| Independent numerical comparisons | 2,983 cases across 41 modules, zero mismatches | Untested inputs, methods or interpretations |
| Jest calculation and regression suite | 1,280 tests in 62 suites | Independent mathematical confirmation by itself |
| Chromium browser checks | 86 checks, including all 65 calculator routes | Safari, Firefox, physical devices or every control combination |
| Code coverage | 95.95% statements, 88.61% branches, 91.76% functions | Correctness of covered code or adequacy of every assertion |
| Continuous integration | Lint, types, tests, build and browser checks passed | Future revisions or production infrastructure outside that run |
Numerical tolerances are defined per fixture and output; there is no site-wide decimal-precision guarantee. Approximate and exact methods can legitimately differ. Values close to a decision threshold require particular care because even a small numerical difference can change a binary significance label. Statistical conclusions also depend on study design, assumptions and data quality.
Technical Implementation
- Test Framework: Jest tests for calculations, parsing and result components, plus browser regression checks
- Reference Software: The 19 September 2026 fixtures use R 4.5.2, SciPy 1.17.1 and NumPy 2.4.5; generators record the applicable versions and conventions
- Distribution Functions: jStat library for probability distributions, checked on selected cases against independent distribution references
- Formulas: Excel/SPSS-compatible formulas for skewness and kurtosis (using the adjusted Fisher-Pearson standardized moment coefficient)
- Tie Corrections: Proper tie handling implemented for Spearman correlation, Kruskal-Wallis, and Wilcoxon signed-rank tests
- Continuous Integration: The checked-in workflow runs linting, type checks, unit tests, the production build and browser regressions on pushes and pull requests; the run for commit
2dbd051passed
Independent Verification
We encourage users to independently verify our results. Reference fixtures include their commands, formulas or generator scripts so their expected values can be checked independently. The source repository documents how to rerun the generators and validation commands.
Questions or Concerns?
If you believe you've found an error in any of our calculators, please contact us with the specific inputs and expected outputs. We take accuracy seriously and will investigate all reported discrepancies.
