Academic Blog

Descriptive statistics explained simply — why the average can mislead, what skewness tells you about income inequality, and how fat tails caused the 2008 financial crisis. A beginner-friendly guide with worked examples, the UK household income case study, and practice questions.

Standard deviation is the single most-used spread statistic in the whole subject, and dividing by n instead of n−1 is the single most common mistake made calculating it. The Statistics Made Simple Practice Questions workbook has a full chapter of drills built around exactly this distinction. Statistics · Variability What is Standard Deviation? The most widely used measure of spread — how...

Picking the wrong measure of central tendency doesn't just cost exam marks — it's how misleading headlines about “average” income or house prices get made. The Statistics Made Simple Practice Questions workbook has a full section of mean/median/mode problems with worked answers. Statistics · Descriptive Statistics Mean, Median and Mode The three measures of central tendency —...

A false positive and a false negative — everyone mixes them up. The “boy who cried wolf” mnemonic that runs Type I then Type II in order, the trade-off nobody explains, why power = 1−β, and why which error to fear is a values judgement, not a formula.

The p-value is the probability of data this extreme assuming the null is true — not the probability the null is true, not the chance your result was luck, not the probability the alternative holds. The one correct definition, the three seductive wrong ones, and why significant doesn’t mean important.

Standard deviation describes your data; standard error describes your estimate. Here’s the difference, the SE = SD/√n formula that connects them, why only one shrinks with sample size, and the error-bar trap that catches everyone.