Student's t-Test (2D)

This 2D companion runs the same Student's t-test math as the 3D original through a flat, reading-first canvas view: a jittered dot plot shows every simulated data point with its group mean marked by a vertical bar, while a second panel plots the t-distribution's probability density with the two-tailed rejection regions shaded in red and the observed t statistic marked with a yellow flag. Three tabs switch between the one-sample test (comparing a sample mean against a fixed null value μ₀), the two-sample test (comparing independent group A vs B, with a toggle between pooled/Student and Welch's unequal-variance formula), and the paired test (comparing before/after measurements on the same subjects via the mean of the differences). Every slider — sample size, means, standard deviations, the null hypothesis, the mean difference — regenerates a fresh simulated sample with a seeded pseudo-random generator and recomputes the t statistic, degrees of freedom, p-value (via the regularised incomplete beta function), 95% confidence interval, Cohen's d effect size and statistical power live, so you can watch exactly how sample size and effect size trade off against significance.