Statistics · Modules 1 to 13

Statistics Study Tools

See statistics happen. Every module turns data into pictures you can watch: samples being drawn, histograms building, bell curves shading, intervals catching the true mean. Walkthroughs include animated worked examples, and every Lab has an explorer, an unlimited practice-problem trainer with hints and worked solutions, a game and real-life cases from health, sports, money and science. Everything runs in your browser on a computer, tablet or phone. No login, nothing graded.

How to use this: open the walkthrough first and go at your own pace with the arrow keys or Next. Then open the Lab: play with the explorer, then practice in the Problem Trainer, using the hints and the animated worked solutions. Use the tools bar at the top of each page to pause the animations, slow them down, have the text read aloud, or get a written description of each picture.

Module 1 Sampling and data

Populations and samples, types of data, study design and the sampling methods that make data trustworthy.

Start here · Animated walkthroughSampling and data WalkthroughWatch simple random, stratified, cluster, systematic and convenience samples being pulled from an animated crowd, then learn data types, levels of measurement, bias, experiment design and frequency tables through animated worked examples. Explorer + practiceModule 1 LabRun a sampling simulator that shows bias and spread on a dot plot, practice unlimited problems with worked solutions, race the clock naming methods and data types, and work through real-life cases from nursing, sports, banking and science.

Module 2 Describing data: graphs, center and spread

Turning raw numbers into graphs and summaries: shape, center, spread and outliers.

Start here · Animated walkthroughDescribing data: graphs, center and spread WalkthroughWatch raw numbers become stem-and-leaf plots, dot plots, histograms and box plots, then see how the mean, median, quartiles, IQR fences and standard deviation are built and where outliers pull them. Explorer + practiceModule 2 LabDrag points to reshape a data set while every summary updates live, practise 16 problem types with worked solutions, race a 60-second shape game, and apply it all to health, money and sports cases.

Module 3 Probability

The rules of chance with coins, dice, cards, Venn diagrams and tree diagrams.

Start here · Animated walkthroughProbability WalkthroughWatch coins, dice, cards, Venn diagrams and tree diagrams animate the core rules of probability, from sample spaces and the law of large numbers through the addition and multiplication rules, conditional probability and Bayes' reasoning with a screening test. Explorer + practiceModule 3 LabRun thousands of simulated flips and rolls, solve unlimited problems with hints and worked solutions, race a 60-second odds game, and apply probability to health, sports, money and everyday decisions.

Module 4 Discrete random variables and the binomial

Random variables, expected value and the binomial distribution.

Start here · Animated walkthroughDiscrete random variables and the binomial WalkthroughSee a die's running average settle at 3.5, then watch probability tables, histograms, tree diagrams and Pascal's triangle build the binomial formula, mean np and SD √(np(1 − p)), with brief geometric and Poisson models. Explorer + practiceModule 4 LabReshape a binomial histogram with sliders, solve unlimited randomly generated problems with animated worked solutions, race the clock turning words into inequalities, and apply it all to health, sports, money and science scenarios.

Module 5 The normal distribution and z-scores

The bell curve, z-scores, areas under the curve and the empirical rule.

Start here · Animated walkthroughThe normal distribution and z-scores WalkthroughWatch probability become shaded area under a bell curve, see μ slide it and σ stretch it, and step through animated worked examples on the empirical rule, z-scores, left, right and between areas, and percentile cutoffs. Explorer + practiceModule 5 LabDrag cutoffs on a live normal curve, solve unlimited problems at three levels with worked solutions, race the clock estimating areas, and apply the normal model to health, sports, money and science cases.

Module 6 Sampling distributions and the Central Limit Theorem

Why sample means behave so well: sampling distributions and the Central Limit Theorem.

Start here · Animated walkthroughSampling distributions and the Central Limit Theorem WalkthroughWatch random samples from skewed, flat and two-humped populations give different means, then see those means pile into a bell curve as n grows. They learn σ/√n, the CLT, z for x̄ and p̂ with the np ≥ 10 check, and the law of large numbers. Explorer + practiceModule 6 LabDraw thousands of samples from any population and watch the histogram fill in under the normal curve, then practise with unlimited problems, a timed SE Sprint and real-life cases.

Module 7 Confidence intervals

Estimating the unknown with a margin of error, and what 95 percent confidence really means.

Start here · Animated walkthroughConfidence intervals WalkthroughWatch 100 confidence intervals drop in from 100 random samples and see about 95 of them capture the true mean, then build z, t and proportion intervals step by step with animated worked examples and learn to choose a sample size. Explorer + practiceModule 7 LabRun an interval factory to watch capture rates and widths respond to the confidence level and n, solve unlimited problems with worked solutions, play Wider or Narrower, and apply intervals to health, polling, sports, money and science cases.

Module 8 Hypothesis testing with one sample

Claims, evidence and p-values: the logic of a one-sample test.

Start here · Animated walkthroughHypothesis testing with one sample WalkthroughPut a claim on trial: they watch a courtroom scale tip, p-values shade in as tail areas under the null curve, the decision flip at α, and Type I and Type II errors, α, β and power play out on overlapping curves, then follow animated z, t and proportion tests and the link to confidence intervals. Explorer + practiceModule 8 LabSet the null, sample result, n and α in a live test explorer, solve unlimited test problems with hints and worked solutions, race the clock giving verdicts, and test real claims from nursing, drug trials, sports, money and science.

Module 9 Comparing two groups

Comparing two groups: independent samples, paired data and two proportions.

Start here · Animated walkthroughComparing two groups WalkthroughWatch two clinics, before-and-after patients and an A/B test become differences, standard errors, t and z statistics, p-values and intervals, with animated worked examples on Welch's t test and interval, the paired t test on differences, and the pooled two-proportion z test and interval for p1 − p2. Explorer + practiceModule 9 LabDrag two dot plots while t, p and the overlap update live, solve 12 types of unlimited problems with worked solutions, race the clock sorting study designs, and interpret clinical trials, A/B tests, sports and science cases.

Module 10 Chi-square tests

Counts in categories: goodness of fit, independence and homogeneity.

Start here · Animated walkthroughChi-square tests WalkthroughWatch candies and die rolls become counts, see expected counts fly into a table, build χ² one cell contribution at a time, and watch the χ² curve change shape with df while the right tail becomes the p-value, through animated worked examples on a die, candy colors, blood types and a two-way table. Explorer + practiceModule 10 LabEdit observed counts and see expected counts, contribution bars, χ², df and the shaded p-value update live, solve 12 types of unlimited problems with worked solutions, race a 60-second χ² Sprint, and apply chi-square tests to nursing, health, sports, money and genetics cases.

Module 11 Correlation and linear regression

Scatterplots, correlation, the least-squares line and residuals.

Start here · Animated walkthroughCorrelation and linear regression WalkthroughWatch points land on a scatterplot, see r built from z-score products as quadrants light up, and watch the residual squares shrink until the least squares line settles, then work through slope, intercept, prediction, extrapolation, residual plots, r squared, influential points and a t test for the slope. Explorer + practiceModule 11 LabClick and drag points while the line, r and the residual squares update live, try to beat the best fit in Guess the line, solve unlimited problems with worked solutions, race to estimate r, and apply regression to health, sports, money and science cases.

Module 12 ANOVA: comparing many groups

Comparing three or more group means with one-way ANOVA.

Start here · Animated walkthroughANOVA: comparing many groups WalkthroughWatch false alarms pile up as t tests multiply, then see group means spread apart against the scatter inside each group as they build SSB, SSW and SST, fill in an ANOVA table, and read the p-value as a right-tail area under the F curve. Explorer + practiceModule 12 LabDrag group means and change the spread while F and the p-value update live, solve unlimited problems with worked solutions, race the clock in F Sprint, and apply ANOVA to nursing, sports, science and money cases.

Module 13 Statistics in health science: risk, odds and screening tests

The numbers behind health research: risk, odds, treatment effects and screening tests.

Start here · Animated walkthroughStatistics in health science: risk, odds and screening tests WalkthroughWatch icon arrays of 100 and 1,000 people turn into prevalence and incidence, risk, relative risk and odds ratios, ARR, RRR and number needed to treat, sensitivity, specificity, PPV and NPV, likelihood ratios, study designs, confounding, bias and forest plots, with animated worked examples on every key calculation. Explorer + practiceModule 13 LabDrive a 1,000-person screening simulator and a two-group risk calculator, solve unlimited problems at three levels with worked solutions, race the clock in Name That Measure, and work through nursing, outbreak, screening, money, sports and research cases.