15 minutes
Measurement and Representation
Does numeric coding make a variable continuous?
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.
Thinking Like an Investigator
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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?
Relationships: Categorical Variables
13 minutes
Categorical Denominators
Among whom is the percentage being calculated?
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?
15 minutes
Effect Magnitude Before Significance
How large is the difference in proportions?
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?
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
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?
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?
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?
Evidence and Investigator Judgment
18 minutes
Hypothesis Testing as Evidence
What does a p-value measure, and what does it not measure?
17 minutes
Investigator Defense
Can you defend the analysis as an investigator?