Every t-test and z-test you've met so far compares means of numeric data. But what happens when your data is categorical — brand preferences, survey responses, pass/fail outcomes? The chi-square test is the tool built for exactly that gap, and it appears constantly across AP Statistics, A-Level and undergraduate exams. The Statistics Made Simple Complete Bundle covers both chi-square test...
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Binomial Distribution Explained: Formula, Examples and When to Use It
Free throw percentages, defect rates on a production line, click-through on an ad — anywhere you count “successes” out of a fixed number of independent tries, the binomial distribution is doing the work behind the scenes. The Statistics Made Simple Complete Bundle covers discrete probability distributions in full, with a dedicated chapter of worked binomial problems. A...
Marginal Analysis: Why Every Marginal Concept Is a Derivative
Marginal cost, marginal revenue, marginal utility, marginal product – four names for one piece of mathematics. Why marginal always means derivative, why fixed costs vanish at the margin, why MC cuts AC at its minimum, and why MR = MC is simply the profit derivative set to zero.
Anchoring Bias in Finance: How It Distorts Investment Decisions and Market Prices
Behavioral Finance · Cognitive BiasAnchoring Bias in FinanceWhy the first number you encounter distorts every financial judgement that follows — and how anchoring silently shapes asset prices, valuations, and investor behaviour.In a famous experiment, Tversky and Kahneman (1974) asked participants to estimate the percentage of African nations in the United Nations. First, they spun a wheel...
Herd Behavior in Financial Markets: Causes, Examples and Economic Effects
Behavioral Finance · Market DynamicsHerd Behavior in Financial MarketsWhy smart investors abandon their own analysis and follow the crowd — and how this collective irrationality creates asset bubbles, crashes, and market contagion.Between 1995 and 2000, the NASDAQ Composite rose 400%. Investors poured money into companies with no revenue, no profits, and sometimes no product — simply because...
Cognitive Biases in Investing: The Complete Guide with Real Examples
Behavioral Finance · Cognitive PsychologyCognitive Biases in InvestingYour brain was not designed for the stock market. Here are the 8 cognitive biases that systematically destroy investor returns — and what the research says about overcoming them.Studies consistently find that average individual investors significantly underperform the market indices they invest in — not because of bad luck,...
Prospect Theory Explained: Why Losses Hurt More Than Gains Feel Good
Behavioral Finance · Decision TheoryProspect Theory ExplainedThe Nobel Prize-winning model that explains why losing £100 feels worse than gaining £100 feels good — and why this asymmetry shapes every financial decision you make.Imagine you're offered two choices: (A) a guaranteed £50, or (B) a 50% chance of £100. Standard expected utility theory says both have the same expected value — and a...
What is Behavioral Finance? How Psychology Shapes Investment Decisions
Financial Economics · Behavioral FinanceWhat is Behavioral Finance?Traditional finance assumes investors are rational. Behavioral finance asks: what happens when they're not? The answer rewrites everything we thought we knew about markets.In 1987, global stock markets crashed by over 20% in a single day. Prices had not changed. No new information had arrived. No economic fundamentals had...
Heteroskedasticity: What It Is, Why It Matters, and How to Fix It
Heteroskedasticity explained simply — your coefficients are still fine, but your standard errors are wrong. A beginner-friendly guide to what causes it, how to detect it with Breusch-Pagan and White tests, and how to fix it with robust standard errors and WLS. Includes the Preston curve case study and practice questions.
Dominant Strategy in Game Theory: Definition, Examples and How to Find It
Game Theory · StrategyDominant Strategy in Game TheoryThe clearest solution concept in game theory — when one strategy is always best, regardless of what anyone else does.In most strategic situations, the best thing to do depends heavily on what your opponent does. But sometimes — and this is what makes these situations especially powerful — one strategy is better than all others no matter what...
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