10 minutes
Choose an Analysis Starting Point
Which statistical approaches fit the outcome, question, and data structure?
Master learning library
Statistical concepts
Explore statistical ideas by theme. Course sessions link to the modules that support that week; new themes can be added here without copying or renaming the underlying modules.
Not sure which analysis fits? Choose the outcome, predictors, goal, and observation structure. Open the interactive guide →Thinking Like an Investigator
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30 minutes
Mapping the Research Process
How do the question, data, code, AI, audit, and interpretation fit together?
14 minutes
AI Is an Assistant, Not an Investigator
What can you delegate without delegating scientific responsibility?
17 minutes
Context Is Part of the Analysis
What happens when project-specific context is missing from an AI-assisted workflow?
19 minutes
The Research Plan Is the Analytical Contract
How can a research specification make intended analysis explicit?
15 minutes
The AI Audit Loop
How do you know an AI-assisted analysis did what you intended?
20 minutes
Build Your Research Specification with AI
How can AI interview you about a plan without inventing the study?
15 minutes
Choosing the Method Is an Investigator Decision
How do you decide whether a recommended method answers your question?
16 minutes
Research Integrity in AI-Assisted Analysis
When does useful AI assistance become a research-integrity problem?
15 minutes
Measurement and Representation
Does numeric coding make a variable continuous?
18 minutes
Hypothesis Testing as Evidence
What does a p-value measure, and what does it not measure?
15 minutes
Statistical Significance vs Policy Importance
Is an association detectable, important, or both?
17 minutes
Investigator Defense
Can you defend the analysis as an investigator?
Samples and Populations
16 minutes
Sampling Variability
Why does an estimate change when the population stays fixed?
17 minutes
Confidence Intervals
What does 95% confidence look like over repeated samples?
18 minutes
Survey Weights and Clustering
Who gets represented, and how much independent information is present?
Data Structure
15 minutes
Cross-Sectional Data
What does one row represent?
16 minutes
Repeated Cross-Sectional Data
What changes in a population when people differ across waves?
17 minutes
Longitudinal (Panel) Data
What changes within the same unit?
16 minutes
Time-Series Data
What changes across time?
16 minutes
Recognizing Clustering in a Dataset
Do observations share a context that makes them more alike?
Data Management
17 minutes
Unit of Analysis
What does one row represent, and what should the analysis compare?
16 minutes
Unit of Treatment
At what level is a policy or intervention assigned?
17 minutes
How a Dataset Represents the Population
What population, time, and process does each dataset represent?
19 minutes
Combining Datasets for Analysis
How can multiple datasets supply the variables at the right analytical level?
15 minutes
One-to-One Merge
When does each key identify exactly one row in both files?
16 minutes
One-to-Many Merge
How can one policy record correctly attach to many observations?
14 minutes
Append Data Files
When do rows from separate files represent the same kind of unit?
15 minutes
joinby and Pair Generation
When should every eligible pair of records be created?
Data Manipulation
19 minutes
Missing Data Decisions
What does missingness mean, and what should the analysis do about it?
17 minutes
Recoding Variables
How can a raw variable be transformed into an analytically meaningful measure?
18 minutes
Generating Variables from Multiple Fields
How should several fields be combined into one defensible variable?
Relationships: Categorical Variables
13 minutes
Categorical Denominators
Among whom is the percentage being calculated?
15 minutes
Ordered-Category and Cumulative-Probability Contrasts
How large is a group difference when the outcome is ordinal?
15 minutes
Effect Magnitude Before Significance
How large is the difference in proportions?
17 minutes
Chi-Square as Evidence of Association
How far are observed counts from independence?
14 minutes
Fisher's Exact Test
What evidence can a small, sparse 2×2 table provide?
12 minutes
McNemar’s Test
Which direction of change is more common in paired binary responses?
16 minutes
Choosing a Categorical Effect Measure
Should the contrast be absolute, relative-risk, or odds based?
15 minutes
Statistical Significance vs Policy Importance
Is an association detectable, important, or both?
Relationships: Continuous Variables and Binary Groups
14 minutes
Reading a Distribution
What can shape reveal before any test is run?
14 minutes
Shape Before Correlation
What relationship can a single correlation coefficient hide?
16 minutes
Pearson and Spearman Correlation
Are we measuring a linear relationship or a monotonic ordering?
14 minutes
Mean, Median, and Extreme Values
When does the mean stop describing a typical observation?
13 minutes
Independent or Paired?
Which observations belong together?
16 minutes
Choosing a Two-Group Comparison
Are you comparing means, paired changes, or relative positions?
17 minutes
Comparing Two Means
How large and how uncertain is the difference in means?
15 minutes
One-Sample t-Test
Is a population mean meaningfully different from a prespecified benchmark?
15 minutes
One-Sample Median Test
Does the population’s middle value differ from a prespecified benchmark?
13 minutes
Comparing Two Medians
How far apart are the middle values of two populations?
18 minutes
Comparing Groups with Ranks
What changes when we replace observed values with their ranks?
16 minutes
ANOVA as a Comparison of Variation
Are group means separated relative to variation within groups?
Causal Reasoning
20 minutes
Epistemology of Causality
What would make a causal claim credible?
15 minutes
Association vs Causation
What claim does the study design support?
17 minutes
Variable Roles
What job does a third variable perform in the analytical argument?
18 minutes
DAG Reasoning for Adjustment
Which path are you trying to block without opening another?
18 minutes
Confounding and Adjustment
How can different group composition distort a crude comparison?
22 minutes
From DAG to Analysis Plan
Can you turn a causal story into a defensible conceptual analysis plan?
Linear Regression
14 minutes
Match the Question to the Method
What quantity does the research question require?
15 minutes
The Two-Group t-Test as Regression
How can a two-group mean difference be written as a model?
15 minutes
Correlation and the Standardized Slope
What does a one-predictor slope add to correlation?
18 minutes
Linear Regression as a Model
What does OLS estimate?
16 minutes
Holding Other Variables Constant
What does holding constant mean?
15 minutes
Residuals
What does a residual reveal?
15 minutes
Linearity of the Conditional Mean
Is a straight-line mean relationship plausible?
15 minutes
Heteroskedasticity
Does outcome variability change across fitted values?
15 minutes
Influential Observations
Does one observation have disproportionate influence?
15 minutes
Collinearity
Can the data distinguish the included predictors?
Logistic Regression
15 minutes
Probability, Odds, and Log-Odds
How can the same chance be expressed on three different scales?
16 minutes
The Logistic Curve
How can a linear predictor produce probabilities between zero and one?
18 minutes
Introducing Multivariable Logistic Regression
How does one model relate a binary outcome to several explanatory variables?
18 minutes
Multinomial Logit and Probit
How can predictors relate to an unordered outcome with three or more categories?
18 minutes
Ordered Logit and Probit
How can a model use the ordering of a categorical outcome?
16 minutes
An Odds Ratio Is Not a Risk Ratio
Why does an odds ratio depend on baseline risk when translated to probability?
17 minutes
Predicted Probabilities
What probability does the fitted model imply for a defined profile or population?
16 minutes
Same-Sample Adjustment
Did the coefficient change because of adjustment or because the sample changed?
19 minutes
Logistic Model Assessment and Selection
Does a candidate model fit adequately and answer the intended question?
Model Refinement and Robustness
16 minutes
Functional Form
How should a predictor enter the model?
15 minutes
Raw and Log Outcome Scales
What does the outcome scale mean?
16 minutes
Sensitivity Analysis
Would a reasonable alternative change the conclusion?
15 minutes
Specification Searching
When does model comparison become specification searching?
Effect Heterogeneity and Interaction
18 minutes
Effect Heterogeneity and Interaction
Does an association differ across groups?
Campbell-Style Causal Designs
18 minutes
Campbell-Style Causal Designs
What design makes a causal comparison credible?
17 minutes
Randomized Pre–Post Designs
What does randomization add to a before-and-after comparison?
18 minutes
Nonrandomized Pre–Post Designs
How does a comparison group turn pre–post change into difference-in-differences?
18 minutes
Interrupted Time Series
Can a level or trend break distinguish policy change from secular time?
18 minutes
Post-Only Comparisons
Can weighting make post-treatment groups comparable without a pre-period?
Rubin-Style Quasi-Experimental Methods
18 minutes
Rubin-Style Quasi-Experimental Methods
How can an observational comparison approximate a counterfactual?
18 minutes
Regression Discontinuity
Can a cutoff create a local comparison that approximates random assignment?
19 minutes
Instrumental Variables
Can outside encouragement identify an effect when treatment is confounded?
18 minutes
Propensity Score Methods
Can observed covariates make treatment groups comparable?
17 minutes
Entropy Balancing
Can weights exactly balance observed covariate moments before estimating an effect?
Difference-in-Differences and Policy Evaluation
20 minutes
Difference-in-Differences: The 2×2 Design
What changed more in the treated group than in the comparison group?
18 minutes
Two-Way Fixed Effects DID
How do multiple treated and comparison units extend 2×2 DID?
17 minutes
Staggered Treatment Timing
What changes when units adopt at different times?
18 minutes
Goodman-Bacon’s Forbidden Comparisons
What comparisons does a TWFE coefficient combine?
19 minutes
Methods for Staggered DID
How can staggered adoption return to clean comparisons?