Intervals for the chi-squared distribution

1. Intervals for the chi-squared distribution

At this point you should be familiar with this diagram

2. Classic inference

which shows how we formulate the null distribution as the distribution of test statistics for data generated in a world where the null hypothesis is true. The procedure is the same when were testing independence using the chi squared statistic its just the shape of the null distribution that changes. To formulate a confidence interval for the chi squared, it makes sense to simply remove the step where we propose a null hypothesis and instead generate data simply through bootstrap resampling.

3. Classic inference

that give us a sampling distribution

4. Classic inference

of the chi squared statistic

5. Classic inference

so that we can formulate an interval

6. Classic inference

to capture the true chi squared parameter but hold on

7. Classic inference

True chi squared parameter? What would that even mean? I know how to think about a difference in two parameters as being a meaningful parameter, but a chi squared? It turns out that the chi squared is only really a useful statistic in the context of a hypothesis test. you're unlikely to ever see a confidence interval here

8. Classic inference

so can just scratch this approach. There you have it. The shortest video ever.

9. Let's practice!

So let's move onto the final chapter in our investigation of categorical data.

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