What's New
The latest StatLens tools, labs, and activities — newest first.
2026-09-07Improved
Type a contingency table straight into Compare Two Categorical Variables
The page’s subject is two variables, but its Edit Data tab only had one-variable
editors — a reviewer trying to enter a 2×2 found nowhere to put it. Data entry
is now an editable r×c grid of counts: name the two variables and
their levels, type the counts, and watch live row, column and grand totals catch
transcription slips. You can also paste a table straight out of Excel or
Word — labels and all — and loading a built-in dataset now fills the grid
with its cross-tabulation, so you can see the table you’re analysing. Case-level
CSV is still there as a second option. Reported by R. Widjaja.
Open the tool →
2026-09-07Improved
Open data from a link — and hand the class a QR code
The Open File tab is now Open File/URL, and takes a link to a hosted CSV, TSV, or JSON alongside the file picker. Loading from a link writes it into the page’s own address, so Share then gives you a QR code that opens the tool with your data already in it — post the file once (a GitHub gist takes a minute and needs no website), project the code, and skip thirty uploads. Suggested by Todd Will. Step-by-step, including the Google Sheets route: Show the class a QR code →
2026-09-06Improved
Sampling Distribution Lab can hide the true parameter
The sampling chapters ask students to estimate a population mean they're told is unknown — while the app printed μ on screen the whole time. Add ?parameter=locked and the true value is withheld: the μ readout, the marker on both charts, and the population line in the results. Use ?parameter=hidden instead and you also get a Reveal the true value button, for driving a demo live — uncover it once the class has committed to an estimate, then hide it again for the next group. The population shape and all three tiers stay visible throughout, and σ/√n stays too, so the theory story is intact. Works in proportion mode as well. Try it →
2026-09-05Improved
CI Coverage now compares four interval methods
The coverage demo already let you switch between the t-interval and the bootstrap percentile interval. It now offers two more — bootstrap ±z·SE and bootstrap BCa — so you can measure, on the same population, how often each construction actually delivers its advertised 95%. Link straight to one with ?method=t, ?method=bootstrap, ?method=se or ?method=bca. What it shows on a right-skewed population is worth seeing: at n = 8 every method under-covers (t 88.4%, percentile 83.7%, ±2·SE 85.3%, BCa 85.8%), the gap to 95% is bigger than any gap between methods, and BCa buys a point or two rather than closing it. Pairs with Why the Percentile CI Works, which argues why the percentile interval should work at all. Open the tool →
2026-09-05New tool
Why the Percentile CI Works
A new conceptual demo that answers the question students (and colleagues) actually ask about the bootstrap: why is the middle 95% of the bootstrap distribution a confidence interval? Build the true sampling distribution from a visible 200-dot population, then freeze one sample and bootstrap from it — both distributions land on the same axis, so you can see that the bootstrap distribution is the sampling distribution slid over to sit at x̄. A slider sweeps the frozen sample's mean across the sampling distribution while the page reports two verdicts side by side: did x̄ land in the central 95%, and did the percentile interval capture μ? They flip together — that agreement is the justification. Switch the population to right-skewed to see where the argument strains, which is exactly what the BCa interval exists to fix. Open the tool →
2026-09-04Feature
BCa bootstrap confidence intervals (expert mode)
Every bootstrap CI page now offers a third method — BCa (bias-corrected and accelerated) — alongside Percentile and ±2 SE. BCa shifts the percentile cutoffs to correct for bias and skew in the bootstrap distribution, so it's the more accurate interval when the distribution isn't symmetric (a skewed mean, a proportion near 0 or 1, a slope). It's an expert-mode option (turn on "Expert mode" in Settings, or add ?ci_method=bca), so the student default stays the plain percentile interval. Available on one-mean, one-proportion, two-means, two-proportions, paired, and slope. The math is validated against R/scipy's BCa.
2026-09-04Improved
Clearer help on every tool — and keyboard editing in the Scatterplot Editor
A site-wide pass on the in-tool help (the ? button). The distribution calculators, the traditional-inference tests, and the explore pages now have help that actually describes their controls instead of a generic one-liner. We also corrected the simulation help so it names the right idea: bootstrap pages estimate a confidence interval, randomization pages compute a p-value — no more mixing the two. The chi-square test help no longer mentions a confidence interval it never had. And the Scatterplot Editor is now fully keyboard-operable: Tab to a point, arrow-keys to move it (Shift for bigger steps), Delete to remove it, and a numeric box to add one — no dragging required. The dataset catalog gained a help panel too.
2026-09-03Feature
Every tool now shows compact Explore / Preview / Download icon buttons in the data summary bar once a dataset is loaded. Preview (grid icon) opens the actual data in a scrollable table — variable labels, types, and rows — without leaving the page; Download (arrow) generates a CSV of the full dataset on demand; Explore (chart) jumps the dataset straight into the right explorer. The same Explore, Preview, and Download icons now sit on every row of the Browse All Datasets catalog too, so an instructor can jump a dataset into the right explorer, look inside it, or grab its CSV without hunting. Great for just seeing what's in a bundled dataset before assigning it. See it on a dataset.
2026-08-18New activity
The first guided activity on a distribution calculator. Guess 8 shuffled cards with 4 symbols and no ESP, so X ~ Binomial(8, 0.25). Students predict the expected number correct (np = 2), see the distribution pile up low, then compute the certification bar — P(X ≥ 6) ≈ 0.004. The payoff: because luck almost never clears that bar, passing it is real evidence — the seed of a p-value. (Also shipped: the binomial calculator now reads ?n, ?p, ?k, ?type for deep-links.) Open the activity.
2026-08-18New activity
The empirical rule made exact, on the Normal calculator. SAT math scores follow X ~ N(609, 80); students predict the area within one SD (≈ 68%) and beyond two SDs (≈ 2.5%), then read the tool's exact areas (0.6827 and 0.0228) and see where the 68–95–99.7 shortcut ends and the calculator takes over. Open the activity.
2026-08-16New activity
A gentle first taste of hypothesis-testing logic, built on the Sampling Distribution Lab. 80 children taste two identical cereals; 52 pick the box with cartoons. Students build the "no preference" distribution (p=0.5, n=80), see that chance alone keeps p̂ between about 0.39 and 0.61, and then find that the real result — p̂=0.65 — sits far out in the tail. A result chance almost never produces is evidence something real is going on. Predict → simulate → weigh the evidence, no formulas. Open the activity.
2026-08-16New activity
The Central Limit Theorem, made visible. Starting from a strongly right-skewed population, students draw the sampling distribution of x̄ at n=5 (still skewed), n=30 (nearly bell-shaped), and n=100 (a clean normal) — then switch to a normal population and watch it turn out bell-shaped even at n=5. The payoff: a skewed population needs a larger n before x̄ looks normal, which is exactly where the n > 30 rule of thumb comes from. Open the activity.
2026-08-16New activity
A guided activity for the Sampling Distribution Lab that makes the success–failure condition tangible. Students predict, then draw, three sampling distributions of p̂: n=10, p=0.4 (skewed & granular — both parts fail); n=100, p=0.6 (a clean normal bell — both pass); and the trap, n=40, p=0.9, where a large np=36 tempts "normal" but n(1−p)=4 keeps it left-skewed. The takeaway lands by seeing it: the CLT needs both np ≥ 10 and n(1−p) ≥ 10, not just one. Open the activity.
2026-08-04New tool
The 2-D analog of the Dotplot Editor. Drag a data point, click empty space to add one, or click a point to remove it — the least-squares line, r, R², slope, and intercept all update live. It's built to make leverage vs. influence tangible: pull a point far out in x and the line chases it; pull it far in y near the middle and it barely budges (an outlier). Toggle a residual overlay and a "high-influence point" flag. First version — try the leverage preset.
2026-08-04New tool
The simulation-first half of goodness-of-fit is here. Give one categorical variable's observed counts and a hypothesized distribution (H0), and the tool repeatedly draws a fresh sample from H0, computes the χ2 statistic each time, and builds the null distribution — your observed χ2 is marked and the p-value is the tail past it. The mechanism strip shows observed counts vs. one simulated sample under H0 with dashed expected-count markers, so students see how sampling variation alone moves the counts. Bundled with Mendel's peas (a famously good fit, p ≈ 0.93), jury composition (a borderline case, p ≈ 0.12), and stock streaks (a geometric-model fit), plus manual entry for any table. Supports the full reasoning-mode embed stack (?plot=only, ?readout=false, ?cutlines=tail, ?observed=off). Its theory-based companion, the Goodness-of-Fit Test (χ2 statistic, df, p-value, expected-count table), completes the Ch. 16 trio — and its Check Conditions panel points back to the simulation when expected counts are small.
2026-07-26Reasoning mode
Every bootstrap and randomization tool now supports a draggable cutoff-line overlay for "read it off the histogram" exercises: instead of counting bars, the student drags a vertical line and reads the tail mass off a live label. ?cutlines=ci gives two lines (drag until each tail hits the confidence level's leftover %, and the line positions are your CI bounds); ?cutlines=tail gives one line to drag to the observed statistic for a p-value. Fully keyboard-drivable (arrow keys, Home/End). Same update also fixes a large-n figure bug — reasoning-mode distributions now always render as a clean, hoverable binned histogram instead of degrading into an unreadable spike cloud when the sample is big.
2026-07-23New tool
Fit Y = β₀ + β₁x₁ + … + βₖxₖ on a bundled or uploaded dataset and read the full software-style output: a coefficient table (estimate, SE, t, p-value, 95% CI) matching summary(lm), the model ANOVA F-test, R² / adjusted R² and residual standard error, and diagnostics (residuals-vs-fitted, residual distribution, and a Cook's-distance flag for high-influence points). To judge multicollinearity, the base view shows a pairwise scatterplot matrix of the predictors; Expert mode adds the VIF metric. The single-predictor slope tool also gained an ANOVA-for-regression table (SST = SSR + SSE, and the F = t² equivalence).
2026-07-14New
Traditional inference now splits estimation from testing, the way the simulation side already does (bootstrap = CI, randomization = test). Six new Confidence Interval pages — for a mean, a proportion, a difference in means, paired differences, a difference in proportions, and a regression slope — each let you set the confidence level with a number box or preset pills, or drag the critical values right on a t- or z-curve. The plot uses the same interactive markers as the distribution calculators (editable probability pills, editable ±critical-value boxes, snap points at common levels), and the results box shows the interval worked out. The Traditional Inference menu and the home-page grids now list a Confidence Interval and a Hypothesis Test entry for each procedure.
2026-07-13Upgraded
Every bootstrap CI page now has a Percentile / ±2 SE / Both toggle next to the confidence level, and it drives the whole page — not just the number in the results box. ±2 SE draws the interval at estimate ± 2·SE over a fitted normal curve; Both overlays the two intervals (dashed dusty-red percentile vs dashed teal normal-approximation) with a legend, so you can see where they agree — and, on a skewed distribution, where they part. The confidence control is now a number box plus 90/95/99 pills accepting any level, the histogram shows symmetric probability pills, and a longstanding bug that drew the theoretical curve wildly out of scale (and the two-group observed statistic in the wrong place) is fixed.
2026-07-06New
In the Two Quantitative Variables explorer, turning on the bands now gives you a real prediction tool. The two bands are clearly distinct — a blue solid confidence band (mean response) inside a wider orange dashed prediction band (a new observation), with a legend. And there's a draggable marker: drag it along the plot (or type a value of x) to see the fitted ŷ, the CI for the mean response, and the prediction interval at that x, updating live. Also: every inference procedure now links out to explore its dataset, and the slope test's "predict a response" box was tidied up.
2026-07-05New
- Linked formulas on every test. The hover-to-highlight linking (value in the formula ↔ its source in the summary/hypothesis) now covers the two-means, paired, one- and two-proportion, and slope tests — not just one-mean.
- Predict a response. The regression-slope test now takes a value of x and reports the fitted ŷ, the confidence interval for the mean response, and the wider prediction interval for a new observation (flags extrapolation). Shareable with
?x0=.
- Multiple Comparisons page. A dedicated Multiple Comparisons route: after the ANOVA F-test, see every pairwise difference with family-wise CIs and adjusted p-values (Tukey HSD or Bonferroni) and a forest plot of which groups differ.
2026-07-05New
A batch of pedagogy improvements:
- Explore → test hand-off. After exploring a dataset, a contextual link carries it straight into the right test — “Test this relationship” from regression (to the slope test), and “Test the difference / these groups” from grouped comparison (to the two-means test or ANOVA), with your variables already selected.
- Comparable group panels. The stacked group histograms now share one y-axis, so a bar of 10 towers over a bar of 4 across groups instead of both filling their panel.
- Two-group bootstrap you can see. The two-means bootstrap now shows each group’s resample as a pluck-and-fly dotplot on a shared axis, with the difference updating live.
- Linked formulas. On the one-mean test, hover (or tab to) a value in the t / CI formula and it lights up everywhere it appears — the sample summary, the null value, its other uses — connecting the math to the data.
2026-07-05Upgraded
The one-sample mean tools — the bootstrap CI and the randomization test — now share one rebuilt mechanism strip with a Tiles view (each value a card, tagged ×N when it's drawn more than once, greyed when it isn't) and a Dotplots view where the resample is plucked from the sample and flies into place, dot by dot. For the randomization test, the shift to the null is shown explicitly: every value visibly slides by the same constant, with a caption explaining the subtraction. The one- and two-proportion bootstraps got a matching marble grid / bar mechanism.
2026-06-27Upgraded
After a significant F-test, the one-way ANOVA tool now shows post-hoc pairwise comparisons — every pair of group means with a family-wise confidence interval and adjusted p-value, plus a forest plot where intervals that miss zero (in red) mark the pairs that truly differ. Toggle between Tukey HSD and Bonferroni.
2026-06-27Upgraded
The regression scatterplot can now shade the 95% confidence band for the mean response (the classic hourglass, narrowest at the mean of x) and the wider prediction band for a single new observation. Flip on "Show CI & prediction bands," or deep-link with ?bands=true.
2026-06-27New data
Fifteen datasets joined the library — including loan50, possum, county (all 3,142 US counties), Florida Lakes (mercury), Insect Sprays, NBA salaries, and several paired and ANOVA examples from the coursepack. Browse any of them in the Data Explorer.
2026-06-20Upgraded
The normal, t, χ², and F calculators now go beyond left/right tails. Between shades the middle band between two independent bounds — so you can finally compute things like P(500 ≤ X ≤ 650) — and Symmetric shades the two outer tails for the classic two-sided view. Every region shows an editable probability, and you can deep-link an exact setup, e.g. ?tail=between&lo=-1&hi=2.
2026-06-19New page
One front door to every guided activity — all 16, grouped by topic, each linking straight into its tool. Reachable from the footer ("Activities", next to "What's new").
2026-06-19Activity
The xkcd jelly-bean comic, made interactive: run 20 tests on things that truly do nothing and watch a false "discovery" appear by chance. Drives home why a lone p < 0.05 is weak when you don't know how many tests were run — and how a stricter threshold (Bonferroni) fights back.
2026-06-19Activity
A guided, gated activity that takes the most common confidence-interval misconception head-on: with the true mean known (μ = 50), students draw many intervals, watch ~95% capture the truth, and confront why "95% confident" is a property of the procedure — not a 95% chance for any single interval.
2026-06-19Activity
The step-by-step "What is a Randomization Test?" walkthrough now runs as a gated activity on the actual two-proportion randomization tool, with the dealt-cards mechanism strip showing the same 35 promotions re-shuffled between groups. (The old standalone page redirects here; the printable instructor guide is preserved.)
2026-06-19Upgraded
Every simulation tool now has a Copy link button that captures the dataset, every toggle (direction, confidence level, statistic, card mechanism, null value, success outcome) and the seed — so an instructor can hand out a link to an exact setup, and a student can share a link that reproduces their result.
2026-06-18New tool
The Gettysburg Address "Sampling Words" activity, made interactive: pick a "representative" sample by eye (it runs biased high) vs. random samples that center on the truth. Shows that a bigger sample doesn't fix bias — only random selection does.
2026-06-18Upgraded
Predict-first gate ("how many of the next 25 miss μ?"), a cat's-eye peaked-likelihood overlay, changing the confidence level now re-widths the same intervals, and a new percentile-bootstrap method that visibly under-covers for small skewed samples.
2026-06-18Upgraded
The p-value now shows its Monte-Carlo margin (p = X/N ± …, narrowing as you add shuffles), states the encoded null next to the shuffle mechanism, and presents the p-value "by construction." Across all five randomization tools.
2026-06-18Upgraded
Every bootstrap chart now pins the observed sample statistic where the distribution centers, and the results panel contrasts the spread of the data (SD) with the much-narrower standard error — countering the common "it centers on the population" and "SD = SE" mix-ups.
2026-06-18Upgraded
The Explore tools (one-categorical, grouped, multi-variable) now accept an external ?csv= file and expose variable pickers, and the inference pages (chi-square, ANOVA, regression) handle multi-column CSVs cleanly too — so a lesson can point any of them at a shared dataset.
2026-06-17New tool
A from-scratch redesign covering both means and proportions: a three-tier population → one sample → sampling distribution view, freeze/compare two sample sizes on one axis, and predict-reveal guided activities.
2026-06-17Activities
Step-by-step gated activities now run alongside any tool, with predict-then-commit questions and live feedback that quotes the tool's actual on-screen result back to the student.
2026-06-13Upgraded
Two-group proportion randomization can show the shuffle as dealt cards (each observation a card; filled = success), with a live Bars ↔ Cards toggle — making "the outcomes are fixed, only the labels move" concrete.
2026-06-08New tools
Simulation-based power (run many studies; watch empirical power and the p-value dance) and a Decision Errors lab (Type I / Type II as the outcomes of repeated one-proportion tests).
2026-06-06New tools
Two intuition-builders: a coin-guessing game that introduces hypothesis-testing logic before the formal framework, and Stump the Chump, which shows real randomness is clumpier than people expect.
2026-04-04New tool
Drag a line to fit a scatterplot, see the residual squares, and compare your fit to the least-squares and least-absolute-deviation best fits.
2026-04-04New tool
Compare three or more groups: a permutation F-test and the classical one-way ANOVA with a conditions checkpoint and the decomposition table.
2026-04-04New tool
Click to add or remove points and watch the summary statistics update live — a hands-on way to build intuition for center and variability.