Statistics Fundamentals

Develop the statistical mindset: probabilistic thinking, population vs sample, signal vs noise, and why correlation doesn't imply causation.

Learn to classify data as categorical vs numerical, nominal vs ordinal, discrete vs continuous, and understand cross-sectional vs time-series data.

Master the mean, median, and mode — when to use each, how outliers affect them, and how skewness shapes their relationship.

Understand range, variance, standard deviation, IQR, and coefficient of variation — how to measure the spread of data.

Master histograms, bar charts, box plots, and scatter plots. Learn to read distribution shapes and spot misleading charts.

Learn sample spaces, events, probability axioms, the complement rule, addition rule, and multiplication rule.

Understand P(A|B), the medical testing problem, intuition traps, the multiplication rule, and the law of total probability.

Master Bayes' Theorem, the mathematical foundation of rational belief updating, priors vs posteriors, base rate fallacy, and Bayesian vs frequentist thinking.

Master the concept of statistical independence, the crucial difference between independence and mutual exclusivity, conditional independence, and why it matters for modeling.

Learn what random variables are, the difference between discrete and continuous, PMF vs PDF vs CDF, expected value, and variance.

Learn the essential probability distributions: Bernoulli, Binomial, Poisson, Uniform, Exponential, and an introduction to the Normal distribution.

Master the bell curve: normal distribution properties, Z-scores, the empirical rule, standard normal, and why normality appears everywhere in statistics.

Understand the CLT — the reason sample means are normal, why statistics works, standard error, and the magic of large samples.

Master random, stratified, cluster, and systematic sampling. Understand selection bias, non-response bias, and survivorship bias.

Learn about estimators, bias vs variance, consistency, the bias-variance tradeoff, and the Law of Large Numbers.

Master confidence intervals: construction, correct interpretation, Z vs t-distribution, CIs for proportions, and common misinterpretations to avoid.

Learn the logic of hypothesis testing: null and alternative hypotheses, one-tailed vs two-tailed tests, significance levels, and the testing procedure.

Understand what p-values really mean (and don't mean), Type I and II errors, statistical power, and the limitations of significance testing.

Master the Z-test, one-sample t-test, two-sample t-test, paired t-test, and chi-square test — with worked examples for each.

Understand p-hacking, the Bonferroni correction, false discovery rates, and why the replication crisis exists.

Understand covariance, Pearson correlation, Spearman rank correlation, and the many pitfalls of interpreting correlation.

Build and interpret regression models: least squares, slope, intercept, R², residuals, and the LINE assumptions.

Extend regression to multiple predictors: interpret coefficients, handle categories with dummy variables, and avoid multicollinearity and overfitting.

Handle skewed data, heavy tails, and outliers. Learn to detect non-normality and choose appropriate alternatives.

Learn rank-based tests that don't assume normality: Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis, and Spearman correlation.

Learn the bootstrap method: resampling with replacement to estimate standard errors and confidence intervals for any statistic without formulas.

Master controlled experimentation: randomization, sample size calculation, statistical vs practical significance, and common pitfalls in A/B testing.

Learn time series fundamentals: trend, seasonality, noise, moving averages, autocorrelation, and why time-ordered data requires special methods.

Apply statistical thinking to real-world decisions: expected value, risk vs uncertainty, decision trees, cost-benefit analysis, and value of information.

Learn to spot and avoid major statistical fallacies: regression to the mean, Simpson's paradox, law of small numbers, cherry picking, and more.

Develop critical thinking skills to evaluate statistical claims: spotting manipulation, understanding study design, relative vs absolute risk, and asking the right questions.

Apply everything you've learned: analyze real datasets, design experiments, debunk misleading claims, and build statistical reports.