Statistics for Researchers
The statistics your reviewers assume you know. Probability, estimation, honest testing, calibrated intervals, regression, and causal inference, built for people whose results have to survive peer review.
You can choose and defend an estimator, state exactly what your p-value and interval do and do not claim, design a study with adequate power, and reason about causation with DAGs instead of hope.
Probability that pays rent
Every statistical claim you will ever make is a sentence in this language; learn the grammar before the rhetoric.
Conditional and marginal thinking is where most published confusion starts, and expectation is the accountant of the whole subject.
Knowing which distribution you are holding, and why averages settle down, is the difference between modeling and matching shapes.
The central limit theorem is why any of this works on real data, and simulation is how you check your intuition without waiting for a proof.
Estimation
Bias, variance, and consistency are the report card every estimator carries; method of moments is the first honest attempt.
MLE is the workhorse of applied statistics, and the Cramer-Rao bound tells you when to stop looking for something better.
The standard error is the most-quoted, least-understood number in science; here is where it actually comes from.
Resampling gives you uncertainty when formulas run out, and M-estimators keep one outlier from owning your conclusion.
Testing, honestly
Type I, Type II, and power are the terms of the bet every test places; most underpowered studies never knew they were betting.
The t, chi-square, and F tests done by hand once each, and what a p-value is and is not, which is the most misstated fact in research.
Twenty tests buy one false discovery at full price; FWER, FDR, and preregistration are how you stop paying it.
Absence of evidence has its own test, and the replication crisis is the case study in what happens when a field skips this stage.
Intervals and calibration
An interval is a procedure with a coverage promise; exact, asymptotic, and bootstrap constructions keep that promise differently.
Confidence intervals speak about parameters, prediction intervals about the next observation; confusing them flatters every forecast.
When 95 percent really means 95 percent, and how to draw uncertainty so the reader hears what you actually know.
Regression
Least squares is a projection, and each assumption is a load bearing wall; know which one fails before the estimate leans.
Residuals, leverage, and influence are the regression's own testimony about itself; learn to take the deposition.
Real data have outliers and real effects have modifiers; robust regression and interaction terms handle both without theater.
AIC, BIC, and cross-validation pick predictive models; none of them make a coefficient causal, and the warning label is part of the method.
Causal inference
The fundamental problem of causal inference has exactly one clean solution, and it is randomization done right.
A directed graph turns arguments about bias into arithmetic; the backdoor criterion is worth a hundred seminar fights.
When you cannot randomize, instruments and cutoffs are the two most credible substitutes, each with a price printed in assumptions.
Parallel trends is an assumption you can almost see, and sensitivity analysis bounds what the confounder you missed could have done.
Capstones
Design, power, preregister, run, analyze, report: the whole discipline in one study you could actually submit.
Confounding is the default state of nature; this capstone is the drill for concluding carefully anyway.
The whole path compressed onto one card you can pin above the desk where the analysis actually happens.