Segment 19. The Chi Square Statistic

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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