Statistics From Zero · Lesson 1 of 22
What Is Statistics Actually For?
In one sentence: 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.
The idea
Imagine a giant pot of chilli. You want to know if it's too salty. You don't eat the whole pot. You stir it, taste one spoonful, and decide.
That's statistics. The whole pot is the population: everything you actually care about. The spoonful is the sample: the small part you can actually check. Statistics is the set of rules for going from the spoon to the pot without fooling yourself.
It does two jobs:
- Describing what you saw: "this spoonful was quite salty". That's descriptive statistics: averages, percentages, charts.
- Guessing about what you didn't see: "so the whole pot is probably quite salty, and here's how sure I am". That's inferential statistics, and it's the part most courses spend the semester on.
Uncle Gary makes chilli
Uncle Gary is in charge of the chilli at the family barbecue. He tastes it from the top of the pot, declares it "perfectly mild" and goes back to his beer.
He didn't stir it. All the chillies had sunk to the bottom. Aunt Linda's first spoonful from the bottom of the pot is still discussed at family gatherings.
Gary's spoonful wasn't too small. It was taken from the wrong place. That's called bias, and no amount of extra tasting from the top would have fixed it.
Same pot, two spoonfuls
Why "stir the pot" is the most important rule
A sample only tells you about the population if every part of the population had a fair chance of ending up in it. Statisticians call this a random sample. Stirring the pot is the kitchen version.
A big sample from the wrong place is worse than useless, because it makes you confident about the wrong answer. A smaller, properly stirred sample usually beats it.
Try it yourself
The student union wants to know how many nights a week students go out. They ask 50 people at the campus bar on a Friday night. The average answer is 4.2 nights a week.
Is 4.2 a good estimate for all students at the university?
Show the answer
No. Everyone they asked was, by definition, out on a Friday night. Students who were at home, at work or in the library had no chance of being asked. The sample was taken from the top of the pot. The real number for all students is almost certainly lower, and asking 500 people at the same bar wouldn't fix it.
The words your lecturer uses
| Lecturer says | It means |
|---|---|
| Population | Everyone or everything you want to know about (the whole pot) |
| Sample | The part you actually measure (the spoonful) |
| Parameter | A number describing the population, usually unknown (how salty the whole pot really is) |
| Statistic | A number calculated from the sample (how salty your spoonful was) |
| Descriptive statistics | Summarising what you measured |
| Inferential statistics | Using the sample to make careful guesses about the population |
| Random sample | Every member of the population had a fair chance to be picked (you stirred) |
| Bias | A sample that is off in a consistent direction (tasting only from the top) |
Three things to remember
- You almost never see the whole population. You see a sample and make a careful guess.
- Where the sample comes from matters more than how big it is. Stir the pot.
- A good statistician always says how sure they are, not just what they think.
Part of Statistics From Zero, a free beginner course by WrongStat. Not a substitute for your lecturer, but hopefully a good translator.