What Is Statistics Actually For?
Statistics is how you say something sensible about a big group when you can only look at a small part of it, and how sure you're allowed to be.
Start the lesson →Learn
Statistics From Zero, for people who got lost in class.
You're not bad at statistics. You were probably taught it in the wrong order, with the formulas first and the ideas never. This free course flips that: the idea first, a real-life example, and only then the words your lecturer uses.
How each lesson works
- The idea in one sentence, before anything else.
- A real-life example, usually involving Uncle Gary and a barbecue.
- A small exercise with the answer hidden until you've had a go.
- "The words your lecturer uses": a translation table for the exam.
- Three things to remember, for the night before.
The lessons
The Average and Its Evil Twins
There are three different 'averages' (mean, median and mode), and picking the wrong one can make a pub full of normal people look like millionaires.
Start the lesson →Spread: Same Average, Very Different Night
The average tells you where the middle is; the spread tells you how far things wander from it, and two pubs with the same average temperature can be a cosy evening or a night of sweating and shivering.
Start the lesson →Probability Without Tears
Probability is a number between 0 and 1 for how often something happens in the long run, and the coin, the dice and the roulette wheel have no memory, so five reds in a row never make black 'due'.
Start the lesson →The Bell Curve, Explained at the Bar
When lots of small, random nudges add up, the results pile up in a bell shape around the average, and then the standard deviation tells you exactly how rare anything is.
Start the lesson →Why Polls Only Ask About 1,000 People
A well-stirred sample of about 1,000 people pins down a whole country to within about 3 points, because what matters is the size of the spoon, not the size of the pot.
Start the lesson →Ice Cream Doesn't Cause Sunburn
Two things moving together (correlation) doesn't mean one causes the other: there may be a hidden third thing behind both, the cause may run backwards, or it may be pure coincidence.
Start the lesson →Is the Coin Rigged? Hypothesis Testing and the P-Value
To decide whether something is real or just luck, assume it's just luck and ask how surprising your result would be; the p-value is that surprise, written as a probability.
Start the lesson →Between Two and Six Pints: Confidence Intervals
A single number from a sample is almost certainly a bit wrong, so a good estimate comes with a range, and the width of that range tells you how much the number is worth.
Start the lesson →How to Lie With Statistics (So You Can Catch It)
Most misleading statistics aren't false; they're true numbers chosen, framed or measured so that they point the wrong way, and a handful of simple questions catches almost all of them.
Start the lesson →Conditional Probability and Bayes, Explained With a Car Alarm
The chance of something depends on what you already know, and when the thing is rare, even a very accurate alarm is usually a false alarm.
Start the lesson →Linear Regression: Drawing the Line (and Knowing Where to Stop)
Regression draws the straight line that best fits your data and tells you how much one thing tends to change when another does, but it only knows about the range of data you gave it.
Start the lesson →Expected Value: What a Bet Is Worth on Average
Expected value is what a choice pays on average if you could repeat it many times; it explains why casinos always win, why insurance can still be sensible, and why a high win rate can lose money.
Start the lesson →The t-Test: Is the Difference Real or Just Noise?
A t-test compares the gap between two averages with how much the data wobbles and how much data there is, and asks whether the gap stands out from the noise.
Start the lesson →Type I and Type II Errors: Why Small Tests Miss Things
Every test can be wrong in two ways, raising a false alarm or missing something real, and a small sample makes the second mistake far more often than most people realise.
Start the lesson →The Chi-Square Test: Is the Die Loaded?
The chi-square test compares the counts you got with the counts you'd expect if nothing interesting were going on, and tells you whether the gap is bigger than chance usually produces.
Start the lesson →The Central Limit Theorem: Why Averages Become Bell Curves
Average enough independent random things together and the average follows a bell curve, whatever shape the individual things had, and it gets narrower in a predictable way as you add more.
Start the lesson →Simpson's Paradox: Better in Every Group, Worse Overall
A trend that shows up in every group can reverse when the groups are combined, because the groups are mixed in different proportions, so always ask what's inside an overall number.
Start the lesson →Percentiles, Quartiles and Box Plots: Reading a Distribution at a Glance
Percentiles tell you where a value sits in the line-up, quartiles cut the line-up into four, and a box plot draws those cuts so you can see the middle, the spread and the oddballs in one picture.
Start the lesson →The Binomial Distribution: How Likely Is 6 Out of 10?
When you repeat the same yes-or-no attempt a fixed number of times, the binomial distribution tells you how likely each possible number of successes is, so you can tell a good day from a real improvement.
Start the lesson →What Is ANOVA? Comparing Three or More Averages at Once
ANOVA compares several group averages in one test by asking whether the differences between the groups are big compared with the ordinary variation inside them, which avoids the false alarms you'd get from running lots of t-tests.
Start the lesson →Statistically Significant Doesn't Mean Important: Effect Size
Statistically significant means a result is probably not luck, not that it's big or worth anything; to know whether it matters, look at the effect size, in real units, with its range.
Start the lesson →