Head First Statistics

Chapter 14. The χ² Distribution: There’s Something Going On...

Sometimes things don’t turn out quite the way you expect.

When you model a situation using a particular probability distribution, you have a good idea of how things are likely to turn out long-term. But what happens if there are differences between what you expect and what you get? How can you tell whether your discrepancies come down to normal fluctuations, or whether they’re a sign of an underlying problem with your probability model instead? In this chapter, we’ll show you how you can use the X² distribution to analyze your results and sniff out suspicious results.

There may be trouble ahead at Fat Dan’s Casino

Fat Dan’s is used to making a tidy profit from its casino-goers, but this week there’s a problem. The slot machines keep hitting the jackpot, the roulette wheel keeps landing on 12, the dice are loaded, and too many people are winning off one of the blackjack tables.

The casino can’t support the loss for much longer, and Fat Dan suspects foul play. He needs your help to get to the bottom of what’s going on.

Let’s start with the slot machines

As you’ve seen before, Fat Dan’s Casino has a full row of bright, shiny slot machines, just waiting to be played. The trouble is that people keep on playing them—and winning.

Here’s ...