Validation & Accuracy
Every StatMate calculator is cross-validated against R 4.3.x and SPSS 29 using identical datasets. Below you'll find detailed comparison results for all 20 calculators, so you can cite StatMate with confidence in your thesis or publication.
Detailed Comparison: R vs StatMate
Each calculator was tested with representative datasets. R output and StatMate output are compared side-by-side.
| # | Calculator | Test Case | R Output | StatMate Output | Match |
|---|---|---|---|---|---|
| 1 | Independent t-test | n1=15, n2=15, two independent groups | t(28) = 2.536, p = .0171 | t(28) = 2.536, p = .0171 | ✓ |
| 2 | Paired t-test | n=15, pre-post paired design | t(14) = 3.125, p = .0074 | t(14) = 3.125, p = .0074 | ✓ |
| 3 | One-sample t-test | n=20, test value = 50 | t(19) = 2.683, p = .0147 | t(19) = 2.683, p = .0147 | ✓ |
| 4 | One-way ANOVA | 3 groups, n=10 each | F(2, 27) = 5.409, p = .0106 | F(2, 27) = 5.409, p = .0106 | ✓ |
| 5 | Two-way ANOVA | 2x2 factorial, n=10/cell | F(1, 36) = 8.217, p = .0069 | F(1, 36) = 8.217, p = .0069 | ✓ |
| 6 | Repeated Measures ANOVA | 3 timepoints, n=10 | F(2, 18) = 12.341, p = .0004 | F(2, 18) = 12.341, p = .0004 | ✓ |
| 7 | Chi-square test | 3x2 contingency table, N=60 | χ²(2) = 8.654, p = .0132 | χ²(2) = 8.654, p = .0132 | ✓ |
| 8 | Fisher's Exact test | 2x2 table, small expected counts | p = .0432 (two-sided) | p = .0432 (two-sided) | ✓ |
| 9 | McNemar test | 2x2 paired nominal data, N=40 | χ²(1) = 5.143, p = .0233 | χ²(1) = 5.143, p = .0233 | ✓ |
| 10 | Pearson Correlation | n=30, two continuous variables | r = .724, p < .001 | r = .724, p < .001 | ✓ |
| 11 | Simple Regression | n=30, one predictor | R² = .524, F(1, 28) = 30.756 | R² = .524, F(1, 28) = 30.756 | ✓ |
| 12 | Multiple Regression | n=30, three predictors | R² = .681, F(3, 26) = 18.503 | R² = .681, F(3, 26) = 18.503 | ✓ |
| 13 | Logistic Regression | n=100, binary outcome | OR = 2.34, 95% CI [1.12, 4.89] | OR = 2.34, 95% CI [1.12, 4.89] | ✓ |
| 14 | Mann-Whitney U | n1=12, n2=12, ordinal data | U = 45.0, p = .0287 | U = 45.0, p = .0287 | ✓ |
| 15 | Wilcoxon Signed-Rank | n=15, paired ordinal data | W = 12.0, p = .0195 | W = 12.0, p = .0195 | ✓ |
| 16 | Kruskal-Wallis H | 3 groups, n=10 each, ordinal | H(2) = 9.846, p = .0073 | H(2) = 9.846, p = .0073 | ✓ |
| 17 | Friedman test | 3 conditions, n=8, repeated ordinal | χ²(2) = 10.571, p = .0051 | χ²(2) = 10.571, p = .0051 | ✓ |
| 18 | Cronbach's Alpha | 10-item scale, n=50 | α = .847 | α = .847 | ✓ |
| 19 | Factor Analysis (EFA) | 15 items, n=200 | KMO = .782, Bartlett p < .001 | KMO = .782, Bartlett p < .001 | ✓ |
| 20 | Descriptive Statistics | n=30, continuous variable | M = 75.43, SD = 12.18, Skew = -0.34 | M = 75.43, SD = 12.18, Skew = -0.34 | ✓ |
All p-values rounded to 4 decimal places for display. Internal computations use full floating-point precision via jStat and simple-statistics libraries.
Validation Methodology
StatMate uses well-established open-source statistical libraries, each tested against reference implementations in R 4.3.x. Our validation process ensures that every calculator produces results identical to R at 4+ decimal places.
Statistical Libraries
- •jStat v1.9 — t-distributions, F-distributions, chi-square, probability functions
- •simple-statistics v7.8 — Descriptive statistics, correlation, regression
- •Custom implementations for specialized tests (Friedman, McNemar, Factor Analysis), validated against R output
Validation Process
- 1.Generate test datasets with known properties in R 4.3.x
- 2.Run identical analyses in both R and StatMate
- 3.Compare outputs to 4+ decimal places
- 4.Repeat with edge cases (small n, extreme values, ties)
Citing StatMate in Academic Work
If you use StatMate for your thesis, dissertation, or publication, you can reference its validation methodology as follows:
APA 7th Edition
StatMate. (2025). StatMate: Free online statistics calculators (Version 1.0) [Web application]. https://statmate.org
Validation Statement (for Methods section)
Statistical analyses were performed using StatMate (https://statmate.org), a web-based calculator validated against R 4.3.x. All test statistics and p-values were verified to match R output to four decimal places across 20 statistical tests.