Segment 12. P-Value Tests

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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/2Ul7TI0B5ek

Links to the slides: PDF file or PowerPoint file

Problems

To Calculate

1. What is the critical region for a 5% two-sided test if, under the null hypothesis, the test statistic is distributed as Failed to parse (unknown error): \text{Student}(0,\sigma,4) ? That is, what values of the test statistic disprove the null hypothesis with p < 0.05? (OK to use Python, MATLAB, or Mathematica.)

2. For an exponentially distributed test statistic with mean Failed to parse (unknown error): \mu (under the null hypothesis), when is the the null hypothesis disproved with p < 0.01 for a one-sided test? for a two-sided test?

To Think About

1. P-value tests require an initial choice of a test statistic. What goes wrong if you choose a poor test statistic? What would make it poor?

2. If the null hypothesis is that a coin is fair, and you record the results of N flips, what is a good test statistic? Are there any other possible test statistics?

3. Why is it so hard for a Bayesian to do something as simple as, given some data, disproving a null hypothesis? Can't she just compute a Bayes odds ratio, P(null hypothesis is true)/P(null hypothesis is false) and derive a probability that the null hypothesis is true?

Class Activity