# 4BUNCO, BRICKS, AND MARKED CARDS: CHI-SQUARED TESTS AND HOW TO BEAT A CHEATER

Imagine you’re in Las Vegas, in a dark room somewhere along the alleyways off the strip. A slick man in a leisure suit smiles at you from across a dimly lit table. You’re playing a dice game called Sixes Bet. Ordinarily, you’d stay away from this game. After all, the odds of winning money at Sixes Bet are grim. But Mr. Slick has turned the tables, and based on your calculations, the probability you’ll win each game is more than a half. The best odds you’ll find anywhere in Sin City.

But if your odds are so good, why is your stack of betting chips getting so small?

Most basic statistical techniques work on continuous data, numeric observations that can take on any real value in some range. But not all observations are continuous, or even, for that matter, numeric. Sometimes you’ve got discrete data—whole numbers, integers, categories, or grouped observations. Analyzing such data takes something different than a sample mean, standard deviation, and t-test.

There are a relatively small number of basic techniques for analyzing discrete data, but these techniques are versatile and can answer many different types of questions. Like whether this greasy man sitting across from you, grinning with satisfaction, is really playing fair or not. This chapter presents common methods for discrete data analysis and shows how the chi-squared test can help you beat a cheater.

## WHAT HAPPENS IN VEGAS … HOW STATISTICIANS ...

Get Beyond Basic Statistics: Tips, Tricks, and Techniques Every Data Analyst Should Know now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.