Statistical Accuracy Verification
We take the accuracy of our statistical calculators seriously. This document details our comprehensive testing methodology and the verification processes we use to ensure our tools produce reliable results.
Verification Summary
Our Verification Methodology
All statistical calculations on this site are verified against R, the gold-standard open-source statistical computing environment used by researchers worldwide. Our automated test suite runs 994 unit tests, including 79 R-verification tests that compare our output directly against R's results for all major calculators.
Each test case includes the exact R command used for verification, ensuring our results can be independently reproduced. Tests are run automatically on every code change to prevent regressions.
Verified Statistical Methods
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
- ✓ 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)
Precision & Accuracy Details
| Calculation Type | Precision vs R | Notes |
|---|---|---|
| Test statistics (t, F, chi-square) | ± 0.0001 | Exact match |
| Correlation coefficients | ± 0.0001 | Exact match |
| P-values (most) | ± 0.0001 | Exact match |
| P-values (t, chi-square, F distributions) | ± 0.0003 | Minor algorithmic differences in jStat library |
| Critical values | ± 0.001 | Exact match |
| Power analysis | ± 0.10 | Uses normal approximation (conservative estimate) |
Note: All precision differences are far smaller than what would affect any statistical conclusion. For example, the maximum p-value difference of 0.0003 would never change whether a result is considered significant at any standard alpha level (0.05, 0.01, 0.001).
Technical Implementation
- Test Framework: Jest automated testing with 994 unit tests across 54 test suites
- Reference Software: R 4.x with standard packages (stats, car) and pwr package for power analysis
- Distribution Functions: jStat library for probability distributions, verified against R's built-in functions
- 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: All tests run automatically on code changes to prevent accuracy regressions
Independent Verification
We encourage users to independently verify our results. Each test case in our verification suite includes the exact R command used, allowing anyone with R installed to reproduce our reference values.
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.