VisuApps
Grasp descriptive and inferential statistics intuitively.
Apps
Four datasets with the same means, variances, r and regression line but completely different shapes. With residual plot, influence measures, a morph that keeps the statistics fixed, and a build mode for your own cloud.
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Many training sets from the same world as a family of models: average model against the truth (bias), spread of the models (variance) and the exact decomposition test error = bias² + variance + noise over polynomial degree or ridge λ.
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Coin, die, biased coin and Cauchy: the running mean enters the ε-tube around μ, with the exact probability of lying inside next to the Chebyshev bound.
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A one-sided test made tangible: H₀ and H₁ distributions, the critical value from α, Type I error (α) and Type II error (β) as areas, the test power and the p-value — slide the effect size and sample size and watch the power rise.
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Repeated samples, stacked confidence intervals — the fraction that covers the true μ matches the confidence level. Against the misconception "95% probability that μ lies in the interval": the statement applies to the procedure, not to the single interval.
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Raw data as draggable points, a histogram above and a boxplot below; mean and median lines. The mean follows the outlier, the median stays robust — with standard deviation, variance, quartiles and IQR live.
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Rebuild 2.0 (preview): location and spread, target parameters n, x̄, s, skewness and kurtosis via sliders.
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Two features, a linear score, a sigmoid surface in 3D: the threshold plane cuts it in a straight line, log loss per point, gradient descent step by step, XOR as the model's limit.
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Fit a distribution to data: deform the model density, see the likelihood contributions of the points, follow the log-likelihood curve with its maximum (the MLE). The foundation behind regression, logistic regression and Naïve Bayes.
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Many tests with no real effect yield "significant" hits purely by chance. The p-value distribution, the family-wise error rate FWER = 1−(1−α)^m, the garden of forking paths and the Bonferroni correction — beware of data dredging and many KPIs.
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Rare, independent events with rate λ: arrivals on a timeline, a histogram of the event count against the Poisson PMF, exponential waiting times. The characteristic property mean = variance = λ — customer arrivals, claims, defects.
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Residual plots, leverage and Cook's distance on the lecture datasets and Anscombe's quartet – one wrong measurement tilts the line.
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A mosaic of prevalence × sensitivity/specificity: why a positive test for a rare disease is often no reason to panic. The false-positive area beats the hit area — posterior P(D∣+) live, the base-rate fallacy made visible.
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Rebuild 2.0 (preview): Bayes' theorem with prevalence, sensitivity and specificity, prior and posterior on an absolute scale.
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In every group the trend rises, lumped together it falls. A confounder reverses the aggregated relationship — group vs. overall regression switchable, an offset slider makes the paradox visible. Aggregation can deceive.
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Rebuild 2.0 (preview): three real cases — kidney stones, Berkeley 1973, exercise & cholesterol. Subgroups as bubbles, equalise the case mix, and a causal panel asking which view is right.
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Two groups as overlaid distributions + boxplots: t-statistic, p-value (exact t-distribution) and Cohen's d. The catch — the same mean difference becomes significant with a smaller σ or a larger n, while the effect stays the same.
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Seven starting distributions from Bernoulli to Cauchy: the exact distribution of the sum or mean turns into a bell as n grows (σ/√n). With the normal approximation and continuity correction, the Berry–Esseen bound and animated samples; Cauchy shows where the theorem fails.
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A contingency table of two categorical variables as a mosaic: cells colored by standardized residual, observed vs. expected, χ² statistic, degrees of freedom and p-value live. Are two variables independent — e.g. department × promotion?
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