# Segment 19. The Chi Square Statistic

Jump to navigation Jump to search

## Contents

#### Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

{{#widget:Iframe |url=http://www.youtube.com/v/87EMhmPkOhk&hd=1 |width=800 |height=625 |border=0 }}

The direct YouTube link is http://youtu.be/87EMhmPkOhk

Links to the slides: PDF file or PowerPoint file

### Problems

#### To Calculate

1. Prove the assertion on lecture slide 5, namely that, for a multivariate normal distribution, the quantity $({\mathbf x-\mathbf\mu})^T{\mathbf\Sigma}^{-1}({\mathbf x-\mathbf\mu})$, where $\mathbf x$ is a random draw from the multivariate normal, is $\chi^2$ distributed.

#### To Think About

1. Why are we so interested in t-values? Why do we square them?

2. Suppose you measure a bunch of quantities $x_i$, each of which is measured with a measurement accuracy $\sigma_i$ and has a theoretically expected value $\mu_i$. Describe in detail how you might use a chi-square test statistic as a p-value test to see if your theory is viable? Should your test be 1 or 2 tailed?