Bayes’ Theorem Explained: Formula, Examples and the Base Rate Fallacy

Statistics

A medical test is 99% accurate and comes back positive. Most people assume they’re 99% likely to have the disease. They’re usually wrong — often dramatically wrong. The Statistics Made Simple Complete Bundle works through this exact paradox and the theorem...

Skewness and Kurtosis: Measuring the Shape of a Distribution

Statistics

Two datasets can share the exact same mean and standard deviation and still look completely different when plotted — because mean and variance say nothing about the shape of a distribution. Skewness and kurtosis fill that gap, and they matter far beyond the...

One-Way ANOVA Explained: Comparing Means Across Multiple Groups

Statistics

You already know how to compare two means with a t-test. But what happens when you need to compare three, four, or ten groups at once? Running t-tests on every pair inflates your error rate fast — and ANOVA is the tool built to solve that exact problem. The...

Sampling Methods in Statistics: Random, Stratified, Systematic and Cluster

Statistics

The most sophisticated statistical test in the world is worthless if the sample it’s built on is biased. Before any confidence interval or hypothesis test matters, the sampling method has to be right — and this is one of the most exam-tested, most...

Chi-Square Test Explained: Goodness of Fit and Test of Independence

Statistics

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...

Binomial Distribution Explained: Formula, Examples and When to Use It

Statistics

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...

Standard Error vs Standard Deviation: What Is the Difference?

Statistics

If you have ever divided by √n when you should not have — or forgotten to when you should — you are in very large company. The Statistics Made Simple Practice Questions workbook has a full chapter of drills built around exactly this distinction. The...

Type I vs Type II Errors: A Simple Way to Remember the Difference

Statistics

This is a topic where recognition beats memorisation — you need to have seen enough scenarios to classify a new one instantly. The Statistics Made Simple Practice Questions workbook drills exactly that, with exam-style questions and full mark schemes. The two...

What Is a P-Value? A Plain-English Explanation With Examples

Statistics

If p-values still feel slippery after you finish this, the cure is repetition on real numbers. The Statistics Made Simple Practice Questions workbook has over a hundred questions on hypothesis testing alone, each with a fully worked answer that shows the method rather...

Heteroskedasticity: What It Is, Why It Matters, and How to Fix It

Econometrics, Regression Analysis, Statistics

Heteroskedasticity Your coefficients are fine — but your standard errors are lying to you What even is heteroskedasticity? Let’s start with an analogy. Imagine you’re trying to predict how much money people spend on food. For someone earning £1,000 a...