Statistics · Probability TheoryThe Central Limit TheoremWhy sample means always tend toward a normal distribution — regardless of the shape of the original population. The most remarkable result in all of statistics.Suppose you're studying the income of taxi drivers in a city. Incomes are heavily skewed — most earn around £25,000 but a few top earners make £80,000+. Now suppose you take random...
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Matrix Algebra for Economists: Operations, Determinants, Cramer’s Rule and Leontief Input-Output Analysis
An economy is a web of industries feeding into one another. Wassily Leontief won a Nobel Prize turning that tangle into a grid you can solve all at once. A complete guide to matrix algebra for economists: operations, the determinant, the inverse, Cramer’s Rule, and the Leontief input-output model — with worked examples, real applications, and exam technique.
Elasticity Mathematics: Point vs Arc Elasticity, Cross-Price Elasticity and the Lerner Index
Elasticity is a precise number with a precise formula — and which formula you use changes the answer. A complete guide to the mathematics of elasticity: the arc (midpoint) method, point elasticity with calculus, why linear demand has changing elasticity, the revenue rule, income and cross-price elasticity, and the Lerner Index as a measure of monopoly power — with worked examples and exam technique.
Correlation vs Causation: Key Differences, Examples and Why It Matters
Statistics · Research MethodsCorrelation vs CausationOne of the most important distinctions in all of science — and one of the most commonly violated in journalism, business, and everyday reasoning.Countries with more chocolate consumption per capita win more Nobel Prizes. Ice cream sales are correlated with drowning rates. Nicholas Cage film releases correlate with swimming pool drownings....
Nash Equilibrium Explained: Definition, Examples and Real-World Applications
Game Theory · Nash EquilibriumNash Equilibrium ExplainedThe single most important concept in game theory — what happens when every player is doing the best they can given what everyone else is doing.In 1950, a 22-year-old PhD student at Princeton submitted a 27-page dissertation that would eventually earn him the Nobel Prize in Economics. John Nash's key idea was deceptively simple: in any...
Type I and Type II Errors in Statistics: Clear Explanation with Examples
Statistics · Hypothesis TestingType I and Type II ErrorsEvery statistical test can make two kinds of mistakes. Understanding them — and the trade-off between them — is essential for interpreting research correctly.When a court finds an innocent person guilty, it has made a terrible mistake. When it acquits a guilty person, it has also made a mistake — of a different kind. Hypothesis testing...
Market Failures, Externalities, and Public Goods: Why Markets Get It Wrong
Market failures explained simply — negative and positive externalities, public goods, the free-rider problem, and why the sugar tax actually worked. A beginner-friendly guide with the Coase theorem, Akerlof’s lemons, the UK sugar levy case study, and practice questions.
Partial Derivatives in Economics: Marginal Products, Multivariable Optimisation and the Chain Rule
Economics is multivariable: output depends on labour and capital, utility on every good at once. The partial derivative is how you isolate one effect while holding the rest fixed. A complete guide: marginal products and utilities, the marginal rate of substitution, second-order and cross-partials, multivariable optimisation, the chain rule, and what the cross-partial says about automation and wages.
How to Interpret Log Coefficients in Regression: The Four Rules
Log-log, log-level, level-log, level-level — what each regression coefficient actually means, why economists take logs of everything, and when the ×100 shortcut breaks. With worked examples and practice questions.
Hypothesis Testing: A Complete Step-by-Step Guide with Examples
Statistics · Hypothesis TestingHypothesis TestingA complete step-by-step guide — from stating your hypotheses to reaching a conclusion, with worked examples from economics and social science.Does a minimum wage increase reduce employment? Does a new teaching method improve test scores? These are empirical questions — and hypothesis testing is the statistical framework that lets us answer them...
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