# Difference between revisions of "Segment 12. P-Value Tests"

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The direct YouTube link is [http://youtu.be/2Ul7TI0B5ek http://youtu.be/2Ul7TI0B5ek] | The direct YouTube link is [http://youtu.be/2Ul7TI0B5ek http://youtu.be/2Ul7TI0B5ek] | ||

− | Links to the slides: [http:// | + | Links to the slides: [http://wpressutexas.net/coursefiles/12.P-ValueTests.pdf PDF file] or [http://wpressutexas.net/coursefiles/12.P-ValueTests.ppt PowerPoint file] |

===Problems=== | ===Problems=== |

## Latest revision as of 14:29, 22 April 2016

#### 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/2Ul7TI0B5ek&hd=1 |width=800 |height=625 |border=0 }}

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 ? 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 (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?