Undergraduate foundations · Early release
Introduction to Statistics
Statistics is the study of what we can learn from incomplete information. That includes measuring uncertainty, making decisions, and knowing when not to trust an answer.
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Curriculum status: A complete first-pass 45-lesson textbook sequence is drafted across four units and fourteen weeks, but lesson-by-lesson editorial review, formal assessments, original video lectures, and learner pilots remain necessary. An ungraded self-check with 33 questions is available; videos and graded assessments are not yet available.
Thinking with and describing data
Empirical questions, measurement, description and responsible visualizations.
- 01Why Statistics?Learning to reason with evidence when the whole story is unavailable. · 7 min readNot marked complete
- 02Data, Variables, and MeasurementThe numbers mean nothing until we decide what they represent. · 8 min readNot marked complete
- 03What Sort of Study Are We Actually Doing?Surveys, observational comparisons, random assignment, blinding, and ethically useful designs. · 12 min readNot marked complete
- 04The Spreadsheet Is Not the StudyUnits, missing values, duplicates, coding decisions, data dictionaries, and reproducibility. · 11 min readNot marked complete
- 05Center and SpreadWhat an average can tell us—and what it can hide. · 10 min readNot marked complete
- 06Visualizing DistributionsBar charts, histograms, skew, and the subtle ways a graph can change the story. · 9 min readNot marked complete
- 07Quantiles, Quartiles, and OutliersA resistant description of a distribution, with a warning about competing conventions. · 10 min readNot marked complete
- 08When a Graph Lies Without Changing a NumberAxis choices, denominators, scales, uncertainty, and visual ethics. · 12 min readNot marked complete
- 09Association and CorrelationTwo variables, one tempting number, and several reasons to be careful. · 11 min readNot marked complete
Sampling, probability, and distributions
Sampling design, conditional probability and probability distributions.
- 10Sampling, Bias, and UncertaintyWhy the way we choose observations determines what we can learn. · 9 min readNot marked complete
- 11How We Choose a Sample Changes the MathematicsSimple random, stratified, cluster, systematic sampling and design effects. · 13 min readNot marked complete
- 12Probability Is a Model, Not a ProphecyEvents, complements, independence, and how to describe uncertainty without pretending to know the future. · 10 min readNot marked complete
- 13How Many Ways Could This Happen?Multiplication rules, combinations, permutations, and the binomial coefficient. · 11 min readNot marked complete
- 14When Knowing One Thing Changes AnotherConditional probability, tree diagrams, independence, and law of total probability. · 12 min readNot marked complete
- 15Bayes' Theorem and the Base-Rate TrapWhy a test can be highly accurate and still produce many false alarms. · 12 min readNot marked complete
- 16The Long-Run Average Is Not a PromiseExpected value, variance, linear transformations, and why risk needs a spread. · 12 min readNot marked complete
- 17Random Variables and the Binomial ModelHow counting successes becomes a probability distribution. · 11 min readNot marked complete
- 18Counting Events That Might Never HappenPoisson counts, rates, exposure, and why independence matters. · 11 min readNot marked complete
- 19Density Is Not ProbabilityContinuous variables, areas under curves, uniform and exponential models. · 12 min readNot marked complete
- 20The Normal DistributionUnderstand bell curves, standardized values, and areas under a density. · 9 min readNot marked complete
- 21The Central Limit TheoremWatch the shape of a sampling distribution emerge from repeated experiments. · 11 min readNot marked complete
Statistical estimation and inference
Uncertainty, estimation, tests, comparisons and resampling.
- 22Confidence Intervals and the Meaning of 95 PercentThe parameter stays still. The intervals move. · 13 min readNot marked complete
- 23When Sigma Is Not Written on the BlackboardStudent t procedures for one population mean when the population spread is unknown. · 11 min readNot marked complete
- 24A Poll's Margin of Error Is Not MagicEstimating a proportion, Wilson intervals, and why coverage differs from representativeness. · 11 min readNot marked complete
- 25Two Samples, Two Sources of UncertaintyComparing group means with Welch's method, and why design matters more than an impressive difference. · 13 min readNot marked complete
- 26Before and After Is Not Two Independent GroupsPaired observations, change scores, matched designs, and paired t inference. · 11 min readNot marked complete
- 27Two Rates, Two Denominators, One QuestionDifferences in proportions, pooled-null tests, and risk measures. · 11 min readNot marked complete
- 28Hypothesis Tests and P-ValuesA p-value does not tell you the probability that your hypothesis is true. · 14 min readNot marked complete
- 29Is This Die Playing by the Rules?Expected categorical counts, chi-square goodness-of-fit tests, and reference distributions. · 11 min readNot marked complete
- 30Two Categories Walk into a Contingency TableAssociation between categorical variables, expected cell counts, and the independence test. · 11 min readNot marked complete
- 31Not Significant Does Not Mean No EffectType I and II errors, power, meaningful effects, and sample-size decisions. · 13 min readNot marked complete
- 32The Nineteen Tests Nobody MentionedMultiplicity, familywise errors, false discovery rates, and pre-specification. · 13 min readNot marked complete
- 33Randomization Tests and the Logic of an ExperimentSometimes we can calculate a p-value simply by rearranging the assignments. · 13 min readNot marked complete
- 34Bootstrapping the Sampling DistributionWhen a sample is all we have, resampling it reveals what the estimate might do. · 14 min readNot marked complete
Models, causal limits, and research practice
Regression, confounding, categorical models and independent research.
- 35Simpson's Paradox and the Missing VariableHow a published medical comparison reverses when we examine a third variable. · 13 min readNot marked complete
- 36Building a Line with Least SquaresA useful model of association, provided we remember what it can and cannot do. · 14 min readNot marked complete
- 37The Data the Regression Line MissedResidual plots, nonlinear patterns, and the trouble with fitting the wrong model well. · 12 min readNot marked complete
- 38A Regression Slope Needs a Standard ErrorSampling uncertainty, slope t tests, confidence intervals, and model diagnostics. · 13 min readNot marked complete
- 39Three Means Enter, One F Statistic LeavesOne-way ANOVA, within-group and between-group variation, and post-hoc comparison. · 13 min readNot marked complete
- 40A Regression for Yes and NoLogistic models, probabilities, odds, coefficients, and responsible interpretation. · 13 min readNot marked complete
- 41Association, Confounding, and Causal ClaimsWhy knowing how observations were produced is more important than a small p-value. · 13 min readNot marked complete
- 42The Observations That Aren't ThereMissing data, changing denominators, and why a data audit belongs before every model. · 14 min readNot marked complete
- 43One Outcome, Several PredictorsAn honest multivariable regression from a real environmental dataset. · 15 min readNot marked complete
- 44Show Your Work, Including the Uncomfortable PartsResearch questions, data provenance, reproducible code, disclosure, and statistical reporting. · 13 min readNot marked complete
- 45A Statistical Investigation from Question to Reproducible ReportBring research design, visualization, estimation, models, and honest conclusions together. · 18 min readNot marked complete