StatCorr — Correlation Workbench
A browser-only teaching workbench for the most-used dependence summary in applied statistics: the correlation coefficient. StatCorr completes the small family of teaching tools developed for undergraduate statistics at Qatar University, alongside StatTables, StatTests, StatRegress, StatCI, and StatPower.
Why a correlation workbench?
In introductory courses the Pearson coefficient $r$ is often introduced as a single number and then immediately overloaded with interpretations — strength, direction, linearity, predictive value, dependence. Students leave the lecture confusing the four. StatCorr keeps the four interpretations visually separate: the scatter plot makes the geometry of the association explicit, the coefficient panel reports its magnitude, the inference panel reports the evidence against $H_{0}: \rho = 0$, and the rank-based panel shows when the linear summary is misleading.
What the app does
Input. Paste a CSV with two numeric variables, load one of the bundled teaching datasets, or use the simulator to draw $n$ observations from a chosen joint distribution (bivariate normal with prescribed $\rho$, monotone-but-non-linear, or contaminated with outliers).
Coefficients reported. For every dataset the app reports three coefficients side by side:
- the Pearson correlation $r = \dfrac{\sum (x_{i}-\bar x)(y_{i}-\bar y)}{\sqrt{\sum (x_{i}-\bar x)^{2}\sum (y_{i}-\bar y)^{2}}}$, with the Fisher-$z$ confidence interval $\tanh!\big(\operatorname{atanh}(r) \pm z_{1-\alpha/2}/\sqrt{n-3}\big)$ and the $t$-test for $H_{0}: \rho = 0$;
- the Spearman rank correlation $\rho_{s}$ — robust to monotone transformations and to outliers — with its asymptotic test;
- the Kendall $\tau$, reported with the exact small-sample distribution when feasible.
Visual output. A scatter plot with the regression line, the marginal histograms, and a $95%$ confidence ellipse for the joint distribution is drawn alongside the coefficient table. A drag-a-point interaction lets students pull a single observation and watch the three coefficients, the regression line, and the $p$-values update — making vivid the difference between a Pearson coefficient that collapses under one outlier and a Spearman coefficient that does not.
Pedagogical use
StatCorr is designed for the lecture in which correlation is introduced and for the practical that follows it. Three exercises map naturally to the app:
- Linear vs. monotone vs. independent. Generate samples from a bivariate normal, from $Y = X^{3}+\varepsilon$, and from $Y = X^{2} + \varepsilon$ on $[-1,1]$. Compare Pearson, Spearman, and Kendall, and discuss why $r \approx 0$ does not imply independence.
- Outlier sensitivity. Pin a Pearson coefficient near $0.9$, then drag a single point far from the cloud and watch $r$ collapse while $\rho_{s}$ and $\tau$ barely move.
- Inference vs. magnitude. With $n = 5$ a sample correlation of $0.6$ is not significantly different from zero; with $n = 500$ a sample correlation of $0.1$ is. The Fisher-$z$ interval makes both statements explicit on a single graph.
Technical notes
The app is a single-page client-side application built with React + Vite: all computation runs in the student’s browser, with no server round-trip and no data leaving the device. Quantiles for the $t$ and standard normal distributions used for inference and for the Fisher-$z$ interval are computed with the jStat numerical library (MIT-licensed). Random samples for the simulator are produced from a high-quality PRNG seeded by the user, so that classroom demonstrations are reproducible across machines. The static bundle is deployed on Netlify; like its siblings it works offline after first load and has no external run-time dependencies.
