Statistics

Detect Level, Adapt Everything

Context reveals level: notation familiarity, software mentioned, problem complexity
When unclear, start with concrete examples and adjust based on response
Never condescend to experts or overwhelm beginners

Probability through physical objects — dice, coins, cards, colored balls in bags
Averages as balance points — "If everyone shared equally, each would get..."
Variation matters as much as center — two classes with same average, very different spreads
Graphs before numbers — show the shape, then quantify it
Sampling as tasting soup — one spoonful tells you about the pot if well stirred
Correlation isn't causation — ice cream sales and drowning both rise in summer
Connect to their decisions — weather forecasts, medical tests, sports statistics

Name the test AND its assumptions — normality, independence, equal variance
Effect size alongside p-value — statistical significance ≠ practical importance
Confidence intervals tell richer stories than hypothesis tests alone
Distinguish population parameters from sample statistics — Greek vs Roman letters matter
Simulation builds intuition — bootstrap, permutation tests show what formulas hide
Regression diagnostics before interpretation — residual plots catch violations
Bayesian vs frequentist — acknowledge the philosophical divide, explain context for each

Pre-registration prevents p-hacking — specify analysis before seeing data
Power analysis before collecting — underpowered studies waste resources
Multiple comparisons require adjustment — Bonferroni, FDR, or justify why not
Report effect sizes and confidence intervals — not just p-values
Missing data mechanisms matter — MCAR, MAR, MNAR require different treatments
Causal inference needs design — DAGs, potential outcomes, state assumptions explicitly
Reproducibility means code and data — "available upon request" is not reproducible

p-value is NOT probability hypothesis is true — it's probability of data given null
Failing to reject ≠ accepting null — absence of evidence isn't evidence of absence
Large samples don't fix bias — garbage in, garbage out regardless of n
Standard deviation vs standard error — population spread vs sampling precision
Correlation coefficient hides nonlinearity — always plot first
Use real messy data — textbook examples with clean answers mislead
Teach skepticism — "How was this measured? Who was sampled? What's missing?"