Find a ToolStatLens ? ⚙

Test whether several group means differ by permuting the labels and recomputing the F statistic.

randomization test · ANOVA · several groups · three or more groups · F statistic · permutation · comparing many means · p-value

Confidence interval for the difference between two proportions, by resampling each group separately.

bootstrap · two proportions · difference in proportions · compare two percentages · success rate · risk difference · confidence interval

Build a confidence interval for a population proportion by resampling your sample with replacement.

bootstrap · confidence interval for a proportion · percentage · rate · resampling · p-hat · margin of error · what fraction · one sample

Build a confidence interval for a population mean by resampling your sample with replacement, thousands of times.

bootstrap · confidence interval for a mean · resampling · average · mean · margin of error · percentile interval · how precise is my average · one sample · x-bar

Confidence interval for a mean difference when each subject is measured twice — resample the differences.

bootstrap · paired data · before and after · matched pairs · mean difference · repeated measures · confidence interval · same subjects twice

Confidence interval for a regression slope, by resampling the (x, y) pairs.

bootstrap · regression slope · line of best fit · confidence interval for slope · scatterplot · linear relationship · resampling pairs

Confidence interval for the difference between two group means, by resampling each group separately.

bootstrap · two groups · difference in means · compare two averages · treatment and control · confidence interval · independent samples

Test whether counts across several categories match a claimed set of probabilities, by simulation.

goodness of fit · chi-square · categories · expected counts · is the die fair · simulation · one categorical variable · p-value

Test independence in a contingency table by shuffling the group assignment and recomputing chi-square.

randomization test · chi-square · contingency table · two-way table · independence · association · categorical variables · p-value

Test whether two quantitative variables are related by shuffling one against the other and recomputing r.

randomization test · correlation · r · association · shuffle · scatterplot · are these related · p-value · linear relationship

Test whether two groups differ on average by shuffling the group labels — the permutation test.

randomization test · permutation test · shuffle · two groups · difference in means · treatment and control · p-value · does the treatment work · experiment

Test whether two groups differ in their success rate by shuffling the group labels.

randomization test · permutation test · shuffle · two proportions · difference in proportions · success rate · p-value · does the treatment work

Test a claim about a single proportion by simulating what chance alone would produce under the null.

randomization test · simulation · one proportion · is it fair · coin · p-value · null hypothesis · chance alone · could this be luck · exact test

Test a mean difference on paired data by randomly flipping the sign of each difference.

randomization test · paired data · before and after · sign flip · matched pairs · mean difference · p-value · same subjects twice

Test a claim about a single mean by shifting the data to the null value and resampling.

randomization test · one mean · single mean · shifted bootstrap · p-value · null hypothesis · is the average different · one sample test

Bootstrap confidence intervals and randomization hypothesis tests, built by simulating thousands of repetitions you can watch and hover.

simulation · bootstrap · randomization test · permutation test · resampling · confidence interval · p-value · shuffle · null distribution

Guess coin flips, then see where your score falls in the distribution of pure guessing — hypothesis testing before the vocabulary.

are you psychic · coin flip · guessing · chance alone · could this be luck · p-value intuition · null distribution · game · ESP

Compare a quantitative variable across groups with side-by-side boxplots, dotplots, and per-group statistics.

compare groups · side by side boxplots · grouped statistics · by group · treatment and control · means by group · comparing distributions

Explore a whole dataset at once — pick variables, switch plot types, and compare several at a time.

data explorer · multiple variables · multivariate · variable picker · explore dataset · choose a plot · EDA workflow

Click a number line to add and remove points, and watch the mean, median, and standard deviation move as you do.

dotplot editor · build a dataset · mean vs median · standard deviation · variability · outlier · resistant · what happens to the mean · sandbox

Summarise and visualise a dataset: one variable or two, quantitative or categorical, with the plots and statistics that go with each.

explore data · summary statistics · descriptive statistics · graphs · histogram · boxplot · scatterplot · bar chart · EDA

Summarise one categorical variable: counts, proportions, and a bar chart.

one categorical variable · bar chart · frequency table · proportion · percentage · counts · pie chart · category

Summarise one quantitative variable: histogram, dotplot, boxplot, mean, median, standard deviation, quartiles.

descriptive statistics · one quantitative variable · mean · median · standard deviation · quartiles · IQR · histogram · boxplot · dotplot · five number summary · centre and spread

Fit a line by dragging it, see your residuals, then compare against the least-squares fit.

regression by eye · fit a line · least squares · residuals · sum of squared errors · line of best fit · guess the line · game

Drag, add, and remove points and watch the regression line, r, R², and slope respond.

scatterplot editor · influential point · leverage · outlier · correlation · regression line · what happens to r · drag points · sandbox

Type a sequence of heads and tails that looks random, then see how it compares to a real one. Real randomness is clumpier than people expect.

stump the chump · fake randomness · runs · streaks · clumpy · human randomness · gamblers fallacy · coin flip · game

Two categorical variables: contingency table, conditional proportions, and a segmented or side-by-side bar chart.

two categorical variables · contingency table · two-way table · cross tabulation · conditional proportion · segmented bar chart · association

Two quantitative variables: scatterplot, correlation, least-squares line, residuals, and R².

regression · scatterplot · correlation · r · least squares line · line of best fit · residuals · R squared · slope · intercept · linear relationship

Build an interval from each of many samples and count how many capture the parameter — what “95% confident” actually counts.

coverage · confidence level · what does 95% mean · capture rate · confidence interval interpretation · repeated sampling · long run

Interactive demonstrations of the ideas behind the methods — sampling distributions, confidence intervals, power, and errors.

concepts · demonstrations · sampling distribution · confidence interval · power · type I error · CLT · teaching demos

Draw sample after sample from a population you choose, and see where a confidence interval’s margin of error actually comes from.

confidence interval · margin of error · repeated sampling · sampling distribution · standard error · why does the bootstrap work · population vs sample · mean

Type I and Type II errors as the two ways a test can be wrong, with the trade-off between them made visible.

type I error · type II error · false positive · false negative · alpha · beta · power · significance level · decision errors · trade-off

Drop balls through a field of pegs and watch the binomial distribution pile up underneath, with the exact probabilities and the normal approximation drawn over it.

galton board · quincunx · bean machine · plinko · binomial distribution · normal approximation · coin flips · number of successes · central limit theorem · probability · bell curve · simulation

Toss a coin or roll a die over and over: the running proportion settles toward what the model predicts, while the running total wanders further from zero.

law of large numbers · long run proportion · running average · coin flip · die roll · expected value · convergence · law of averages · gamblers fallacy · is the coin due · probability

Run a study over and over and watch how often it detects a real effect — power, as a fraction you can see.

power · sample size · effect size · type II error · how many subjects do I need · detect a difference · alpha · study design

Pick a “representative” sample by eye, then compare it with a random one — bias you can see in your own choices.

sampling bias · convenience sample · random sample · representative · Gettysburg address · biased · why randomise · sampling

Simple random, stratified, cluster, and convenience sampling compared on the same population, with their costs and their spread.

sampling designs · simple random sample · stratified · cluster sampling · convenience sample · multistage · study design · how to sample

Pick a population, set the sample size, and watch the sampling distribution of a mean or proportion build up.

sampling distribution · central limit theorem · CLT · standard error · sample size · population vs sample · x-bar · p-hat · why does the shape change

You never have the true standard error. See what substituting s for sigma, or p-hat for p, costs the interval — and why t* repairs one and nothing repairs the other.

t star · critical value · why t instead of z · 1.96 · margin of error · sigma unknown · sample standard deviation · degrees of freedom · confidence interval width · t distribution · coverage · proportion confidence interval · success-failure condition · np at least 10 · estimated standard error · Wald interval · why simulate

The argument behind every “statistic ± 2 SE” interval, drawn with no numbers on the axis at all.

two standard errors · empirical rule · 68 95 99.7 · confidence interval · margin of error · why plus or minus 2 · capture · standard error

The bootstrap distribution and the true sampling distribution on one axis — why a percentile interval works, and where it strains.

bootstrap · percentile interval · sampling distribution · why does the bootstrap work · shift · plug-in principle · standard error

Chi-square goodness-of-fit test: do observed counts match the claimed probabilities?

goodness of fit · chi-square · expected counts · categories · is the die fair · one categorical variable · p-value

Chi-square test of independence for a two-way table, with expected counts and contributions.

chi-square test · independence · two-way table · contingency table · expected counts · categorical · association · p-value

Confidence interval for the difference between two population means.

confidence interval for a difference in means · two groups · margin of error · t interval · compare two averages

Confidence interval for the difference between two population proportions.

confidence interval for a difference in proportions · two groups · margin of error · z interval · compare two rates

Confidence interval for a population mean using the t distribution.

confidence interval for a mean · t interval · margin of error · critical value · t star · estimate the average

Confidence interval for a mean difference on paired data.

confidence interval · paired data · mean difference · before and after · matched pairs · t interval

Confidence interval for a population proportion using the normal approximation.

confidence interval for a proportion · z interval · margin of error · critical value · z star · estimate a percentage

Confidence interval for a regression slope.

confidence interval for a slope · regression · t interval · margin of error · linear relationship

What happens to error rates when you run many tests, and how Bonferroni and friends respond.

multiple comparisons · Bonferroni · family-wise error · false discovery · many tests · post hoc · p-hacking · adjusted p-value

Multiple linear regression: fit a model with several predictors and read standard software output.

multiple regression · multiple linear regression · several predictors · coefficients · adjusted R squared · model output · MLR

One-proportion z-test for a claim about a population proportion.

one proportion z-test · z test · proportion · percentage · success rate · p-value · normal approximation · is it fair

One-sample t-test for a population mean, with conditions, test statistic, and p-value.

one sample t-test · t test · mean · hypothesis test · p-value · test statistic · degrees of freedom · is the average different

One-way ANOVA: an F-test for whether several group means differ, with the decomposition table.

ANOVA · F test · several groups · three or more groups · sum of squares · mean square · comparing many means · p-value

Paired t-test on the differences when each subject is measured twice.

paired t-test · before and after · matched pairs · mean difference · repeated measures · dependent samples · same subjects twice

T-test for a regression slope: is there a real linear relationship?

regression slope t-test · slope · is the relationship real · linear regression · p-value · standard error of slope · scatterplot

Theory-based confidence intervals and hypothesis tests using the t, z, F, and chi-square distributions, with conditions checked.

traditional inference · t-test · z-test · formula based · theory based · confidence interval · hypothesis test · conditions · central limit theorem

Two-proportion z-test for a difference between two success rates.

two proportion z-test · difference in proportions · compare two percentages · pooled proportion · p-value · risk difference

Two-sample t-test for a difference in means, with Welch and pooled options.

two sample t-test · difference in means · compare two groups · Welch · pooled variance · p-value · independent samples

Probabilities for a number of successes in a fixed number of independent trials.

binomial distribution · exactly k successes · coin flips · number of successes · probability · n and p · discrete distribution

Areas and critical values under a chi-square curve.

chi-square distribution · chi square table · degrees of freedom · critical value · right skewed · goodness of fit

Look up probabilities and critical values on the normal, t, chi-square, F, and binomial distributions.

distribution calculator · probability · critical value · table replacement · normal table · t table · area under the curve

Areas and critical values under an F curve with two degrees-of-freedom parameters.

F distribution · F table · ANOVA · numerator degrees of freedom · denominator · critical value · variance ratio

Areas and critical values under a normal curve, with draggable boundaries.

normal distribution · z score · bell curve · standard normal · area under the curve · z table · percentile · critical value

Null and alternative distributions side by side, with Type I error, Type II error, and power shaded.

power · type I error · type II error · alpha · beta · effect size · sample size · two distributions · shaded regions

Areas and critical values under a t curve for any degrees of freedom.

t distribution · t score · degrees of freedom · t table · critical value · t star · heavier tails

Practise writing formal and plain-language conclusions for a completed test.

writing conclusions · interpretation · formal conclusion · plain language · p-value interpretation · practice · how do I write it up

See a scatterplot, guess the correlation, and find out how close you were.

guess the correlation · r · scatterplot · estimate correlation · game · practice · how strong is the relationship

Short repeatable exercises that build intuition and skill.

practice · games · drills · build intuition · quiz yourself

Turn a file or a pasted table into a StatLens link you can hand to students.

dataset builder · upload csv · make a link · custom data · paste data · share a dataset · instructor tool

The datasets bundled with StatLens, with their variables, sources, and the tools that accept them.

datasets · data · sample data · variables · sources · IMS datasets · openintro

Datasets contributed by instructors, hosted here and loadable by link.

extra datasets · contributed data · instructor datasets · custom data · csv link

Guided step-by-step activity panels that attach to a tool page — predict, run, and confront.

activities · guided · walkthrough · lesson · step by step · predict then reveal · classroom activity

How to use StatLens in a course: linking, seeding for graded work, embedding, and the instructor tools.

for instructors · teaching · course integration · embed · seed · LMS · Canvas · MyOpenMath · assignments

Instructor utilities: the tool catalog, link building, and dataset preparation.

instructor tools · link builder · tool catalog · dataset tools · teaching utilities

How StatLens lines up with Introduction to Modern Statistics, chapter by chapter.

IMS · Introduction to Modern Statistics · openintro · textbook mapping · course alignment