Segment 19. The Chi Square Statistic

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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.)

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 Failed to parse (unknown error): ({\mathbf x-\mathbf\mu})^T{\mathbf\Sigma}^{-1}({\mathbf x-\mathbf\mu}) , where Failed to parse (unknown error): \mathbf x is a random draw from the multivariate normal, is Failed to parse (unknown error): \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 Failed to parse (unknown error): x_i , each of which is measured with a measurement accuracy Failed to parse (unknown error): \sigma_i and has a theoretically expected value Failed to parse (unknown error): \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?


Class Exercise

Class Exercise

Data file: Media:mv_chi.txt