Statistics is where R stops
being a calculator and
starts arguing.
Every test on this path answers one nervous question: could this just be luck? You will learn to put a number on that doubt, and to defend it.
probability → inference → regression → Bayesian, then a certificate track if you want to prove it.
# did group B really score higher, or did we get lucky? t.test(scoreB, scoreA, alternative = "greater")
The order I would teach it in
seven posts · about a weekNot the table of contents. These seven, in exactly this sequence, are the spine of the whole path. Each one only makes sense because the one before it landed. Read them in order and the rest of the path falls into place.
Probability, simulation-first →
Before any formula. We roll the dice ten thousand times in R and let probability emerge from the counting. Get this and nothing later feels like magic.
The Central Limit Theorem →
The single most useful fact in the subject, and the reason a bell curve keeps turning up uninvited. Average enough of anything and it goes normal. Watch it happen.
Hypothesis Testing →
The grammar of every test that follows: null, alternative, p-value, decision. Learn it once here, carefully, and you have learned half of applied statistics.
t-Tests →
Your first real test, and the one in the demo above. Two groups, one honest question: is the difference more than noise? Everything heavier is a variation on this move.
Confidence Intervals →
The grown-up answer. A p-value says maybe not luck; an interval says how big the effect plausibly is. Report these, not bare p-values, and people trust you more.
Linear Regression →
Where it all comes together: a line that is itself a hypothesis test, with a slope you can defend. From here, almost every model you will ever fit is a relative of this one.
Bayes' Theorem →
The other way to argue from data, and worth meeting early even if you stay frequentist. It reframes everything above as updating a belief. Optional, but it makes you sharper.
A p-value is not a verdict. It is how surprised you are allowed to be if nothing is really going on.what the t-Tests post above will teach you to mean by it
The full path, by family
Once the seven above have clicked, here is the rest, grouped the way the subject actually divides. Browse by the question on your desk. Every page runs in the browser.
Probability
11The language of chance, built from simulations up.
- Probability Axioms
- Conditional Probability
- Random Variables
- Binomial vs Poisson
- Normal, t, F, Chi-Squared
- Sampling Distributions
- Expected Value and Variance
Inference and Testing
28Estimating, deciding, and knowing which test to reach for.
- Choosing the Right Test
- Maximum Likelihood Estimation
- Type I and II Errors
- Power Analysis
- Effect Size
- Proportion Tests
- Nonparametric Tests
- Bootstrap (boot package)
Regression
21Lines, curves, and odds, all defended with the same machinery.
- Simple Linear Regression
- Multiple Regression
- Regression Assumptions
- Regression Diagnostics
- Logistic Regression (glm + ROC)
- Poisson Regression
- Ridge and Lasso
- Polynomial and Splines
ANOVA and Design
11Comparing many groups, and designing the experiment first.
- One-Way ANOVA
- Two-Way ANOVA
- Post-Hoc Tests After ANOVA
- Repeated Measures ANOVA
- ANCOVA
- Experimental Design
- A/B Testing
Multivariate
12Many columns at once: reduce them, group them, see them.
- PCA with prcomp()
- Interpreting PCA Output
- Clustering (k-Means / HC / DBSCAN)
- Exploratory Factor Analysis
- SEM and CFA (lavaan)
- Linear Discriminant Analysis
- t-SNE and UMAP
Bayesian
19The other lens: priors, posteriors, and honest uncertainty.
- Bayesian Statistics
- Conjugate Priors
- MCMC in R
- Gibbs Sampling
- Stan
- brms
- Bayesian Linear Regression
- Hierarchical Models
By the end, you can
- Pick the right test for a question without guessing or googling.
- Read a p-value out loud and say what it does and does not mean.
- Fit and defend a regression, assumptions checked, slope interpreted.
- Report a confidence interval and effect size, not a bare significance star.
- Compare many groups with ANOVA and follow up honestly.
- Know when a Bayesian answer fits the question better than a frequentist one.
Statistics exercise hubs
Reading is not knowing. Hypothesis testing, t-tests, ANOVA, regression and more, as auto-graded problem sets with hints when you stall.
Open the exercise hubsThe Statistics certificate track
Two mastery quizzes anchor this path. Pass them and the rest and you earn a verifiable Statistics-with-R credential you can actually link to.
See how the track worksFinish the Statistics track, earn a credential
that says you can actually do this.
Every tutorial on this path stays free. Pro is for the proof: graded mastery quizzes on the path above, a verifiable certificate with your name on it, and a public link a recruiter can click. You earn it by passing the quizzes.
Start with the dice. Roll them ten thousand times, and let the rest of statistics follow.
Begin with Probability