Statistics and Inference

Mean, median, mode, range, variance, standard deviation, quartiles and IQR, computed by hand.

Third and fourth standardised moments, what they say about shape, and how to read them off a histogram.

Assumes: Descriptive Statistics

Simple random, stratified, cluster and systematic sampling, and the biases each introduces.

The distribution of a statistic, standard error of the mean, and the finite population correction.

Assumes: The Central Limit Theorem

Bias, variance, mean squared error, consistency, efficiency and sufficiency.

Assumes: Sampling Distributions and Standard Error

Writing a likelihood, log-likelihood tricks, and deriving MLEs for Bernoulli, normal and Poisson by hand.

Assumes: Point Estimation and Estimator Properties

Matching sample to population moments, and comparing the resulting estimators with MLE.

Assumes: Maximum Likelihood Estimation

Prior to posterior updates, beta-binomial and normal-normal conjugacy, MAP vs posterior mean.

Assumes: Maximum Likelihood Estimation · Gamma and Beta Distributions

Constructing intervals for means and proportions, what 95% actually means, and the width/confidence trade-off.

Assumes: Sampling Distributions and Standard Error

Null and alternative hypotheses, test statistics, rejection regions, p-values and how to interpret them honestly.

Assumes: Confidence Intervals

The error trade-off, computing power, and determining the sample size a study needs.

Assumes: The Hypothesis Testing Framework

One- and two-sample z-tests for means and proportions, with full numeric walkthroughs.

Assumes: The Hypothesis Testing Framework

One-sample, two-sample pooled, Welch and paired t-tests, and choosing between them.

Assumes: The z-Test · t, Chi-Squared and F Distributions

Goodness-of-fit and tests of independence on contingency tables, with expected-frequency calculations.

Assumes: The Hypothesis Testing Framework

Comparing variances, one-way and two-way ANOVA, sum-of-squares decomposition and post-hoc tests.

Assumes: t-Tests

Sign, Wilcoxon, Mann–Whitney, Kruskal–Wallis and Kolmogorov–Smirnov tests, and when to prefer them.

Assumes: t-Tests

Family-wise error rate, Bonferroni, Holm, and Benjamini–Hochberg FDR control.

Assumes: Type I/II Errors, Power and Sample Size

Testing Pearson correlation, Spearman and Kendall alternatives, and the dangers of correlation mining.

Assumes: Covariance and Correlation · t-Tests

Standard errors of coefficients, t and F tests in regression, R², residual plots and influence measures.

Assumes: F-Test and ANOVA · Least Squares and the Normal Equations

Bootstrap confidence intervals, the jackknife, and permutation tests that need no distributional assumption.

Assumes: Confidence Intervals

Randomisation, blocking, factorial designs, confounding and replication.

Assumes: F-Test and ANOVA

Designing an online experiment end to end: metrics, guardrails, peeking, novelty effects and sequential tests.

Assumes: Type I/II Errors, Power and Sample Size

Confounding, Simpson's paradox, causal DAGs, randomised vs observational studies, and simple adjustment strategies.

Assumes: Design of Experiments