Learn statistics
Start with a guided sequence, or go directly to the topic you need. 41 lessons, with worked examples and connections to the tools.
Suggested reading paths
These are reading sequences, not graded courses. Take them in order or start where your question begins.
Understand your dataDefine the question, classify variables, and summarize a distribution.6 lessons
- Introduction to Statistics12 minutes
- Types of Data12 minutes
- Data Collection Methods12 minutes
- Measures of Central Tendency12 minutes
- Standard Deviation and Variance15 minutes
- Data Visualization12 minutes
From probability to normal tablesWork with events, conditional probabilities, distributions, and tail areas.7 lessons
- Introduction to Probability12 minutes
- Probability Rules12 minutes
- Conditional Probability and Independence12 minutes
- Bayes' Theorem12 minutes
- Random Variables12 minutes
- The Normal Distribution18 minutes
- Z-Scores and Standardization15 minutes
Estimate and compareConnect sampling uncertainty to intervals, tests, and practical conclusions.8 lessons
- Sampling Methods12 minutes
- Sampling Distributions18 minutes
- Confidence Intervals20 minutes
- Introduction to Hypothesis Testing20 minutes
- t-Distribution12 minutes
- T-Tests: Comparing Means25 minutes
- Chi-Square Tests20 minutes
- ANOVA: Analysis of Variance20 minutes
Analyze relationshipsRead scatter plots, calculate correlation, and assess regression models.6 lessons
- Reading Scatter Plots and Correlation12 minutes
- Correlation Analysis18 minutes
- Simple Linear Regression25 minutes
- Regression Diagnostics15 minutes
- Multiple Regression15 minutes
- Logistic Regression15 minutes
Put the lessons into practice
Follow one dataset through twelve questions about design, calculation, uncertainty and reporting. Save progress in this browser and see an explanation for every answer.
Start the guided analysis →Foundations
Define the question, observational units, and variables before analyzing.
Introduction to Statistics
Learn the fundamentals of statistics, including what statistics is, why it matters, and the key concepts you need to know to get started.
12 minutes
Types of Data
Classify variables by what they measure. Use worked examples to choose summaries and avoid treating category codes as quantities.
12 minutes
Data Collection Methods
Design a useful study: define the target, distinguish observation from intervention, and handle sampling, missingness and measurement.
12 minutes
Summarizing Data with Tables
Build frequency and two-way tables with clear denominators, ordered cumulative counts and an explicit treatment of missing data.
12 minutes
Descriptive Statistics
Describe the center, spread, shape, and position of observations.
Measures of Central Tendency
Master the three main measures of central tendency: mean, median, and mode. Learn when to use each measure and how to calculate them.
12 minutes
Standard Deviation and Variance
Learn to measure data spread using variance and standard deviation. Understand when and how to use these statistics.
15 minutes
Percentiles and Quartiles
Calculate percentiles and quartiles using an explicit convention. Interpret ranks, IQR and box-plot flags without confusing them with percentages.
12 minutes
Data Visualization
Choose graphs that answer the question. Read distributions, denominators and axes, and spot misleading scales or hidden subgroups.
12 minutes
Z-Scores and Standardization
Master z-scores to compare values across different distributions. Learn standardization, the empirical rule, and how to use z-tables.
15 minutes
Probability
Work with events, conditional information, and counting.
Introduction to Probability
Define outcomes and events, calculate probabilities with a stated model, and distinguish equally likely outcomes from observed frequencies.
12 minutes
Probability Rules
Use complements, overlap corrections and conditional multiplication. Work through a two-way example and distinguish independence from exclusivity.
12 minutes
Counting Principles and Combinatorics
Choose combinations or permutations by whether order matters and replacement is allowed. Derive probabilities from equally likely selections.
12 minutes
Conditional Probability and Independence
Read conditional probabilities with the right denominator. Use a two-way table to distinguish reversed questions and independence.
12 minutes
Bayes' Theorem
Reverse conditional probabilities using base rates. Work through a file-classification example with counts and test prior sensitivity.
12 minutes
Distributions
Choose probability models and understand their assumptions.
Random Variables
Define a numerical outcome and distinguish mass, density and cumulative probability. Calculate expected value and variance from a simple distribution.
12 minutes
Binomial Distribution
Model a fixed number of independent success/failure trials. Calculate exact and cumulative probabilities, and check when the model fails.
12 minutes
Discrete Probability Distributions
Choose a model for counts from its sampling process. Compare binomial, Poisson, geometric, negative binomial and hypergeometric conventions.
12 minutes
Continuous Probability Distributions
Calculate interval probabilities from densities and CDFs. Compare uniform, exponential and other continuous models with units and assumptions.
12 minutes
The Normal Distribution
Understand the most important distribution in statistics. Learn the properties of the bell curve, its parameters, and why it appears everywhere.
18 minutes
t-Distribution
Learn about Student's t-distribution, its relationship to the normal distribution, and when to use t instead of z for statistical inference.
12 minutes
Sampling and Estimation
Connect the sampling design to uncertainty and study planning.
Sampling Methods
Choose a sampling design, identify coverage and nonresponse bias, and distinguish stratified, cluster, systematic and convenience samples.
12 minutes
Sampling Distributions
Understand sampling distributions and the Central Limit Theorem. Learn why sample means enable statistical inference.
18 minutes
Point Estimation
Understand an estimate as a data-based rule. Compare bias, variance and consistency, and pair point estimates with uncertainty and design checks.
12 minutes
Confidence Intervals
Learn how to construct and interpret confidence intervals for population parameters. Understand margin of error and confidence level.
20 minutes
Sample Size Determination
Learn to calculate required sample size. Understand margin of error, confidence level, power analysis, and planning studies.
18 minutes
Hypothesis Testing
Compare evidence with a null model and report practical meaning.
Introduction to Hypothesis Testing
Learn the framework for hypothesis testing: null and alternative hypotheses, test statistics, p-values, and drawing conclusions.
20 minutes
One-Sample Tests
Learn to perform one-sample hypothesis tests. Master z-tests, t-tests, and proportion tests for single populations.
15 minutes
T-Tests: Comparing Means
Master one-sample, two-sample, and paired t-tests. Learn when to use each test, formulas, examples, and how to interpret results.
25 minutes
Two-Sample Tests
Learn to compare two groups with hypothesis tests. Master independent t-tests, paired t-tests, and two-proportion tests.
18 minutes
Chi-Square Tests
Learn how to perform chi-square tests for independence and goodness of fit. Complete guide with formulas, examples, and step-by-step calculations.
20 minutes
ANOVA: Analysis of Variance
Compare means across three or more groups using ANOVA. Learn the F-test, post-hoc analysis, and effect size measures.
20 minutes
Regression
Analyze relationships, fit models, and inspect what they miss.
Reading Scatter Plots and Correlation
Learn to read direction, form, clusters, and influential points in scatter plots before interpreting a correlation coefficient.
12 minutes
Correlation Analysis
Understand correlation coefficients, their interpretation, and limitations. Learn Pearson, Spearman, and point-biserial correlations.
18 minutes
Simple Linear Regression
Learn to fit and interpret linear regression models. Understand least squares, coefficients, predictions, and model assessment.
25 minutes
Regression Diagnostics
Use residual, leverage and influence checks to assess regression. Distinguish model assumptions from design and validate predictions honestly.
15 minutes
Multiple Regression
Interpret adjusted regression coefficients, distinguish prediction from causation, and check interactions, collinearity and evaluation leakage.
15 minutes
Logistic Regression
Interpret logistic coefficients on the odds scale, convert logits to probabilities, and check calibration, separation and causal limits.
15 minutes
Advanced Topics
Explore alternative methods and more complex questions.
Effect Size and Statistical Power
Go beyond p-values to understand practical significance. Learn effect size measures, power analysis, and sample size planning.
18 minutes
Non-Parametric Tests
Learn distribution-free statistical tests for when parametric assumptions fail. Master Mann-Whitney, Wilcoxon, and Kruskal-Wallis tests.
20 minutes
Introduction to Bayesian Statistics
Update a probability distribution using a likelihood and prior. Work through beta-binomial inference and interpret a credible interval conditionally.
15 minutes
Introduction to Time Series Analysis
Analyze ordered observations, compare forecasts with honest baselines, and avoid leakage, automatic stationarity claims and misleading error metrics.
15 minutes