Statistical Hypothesis Testing

 

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Big Ideas

 

 

 

 

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p-values: Take the test!

True or False?

  1. The p-value is the probability that the null hypothesis is true.

     

  2. The p-value is The probability that the alternative hypothesis is true.

     

  3. The p-value is the likelihood of the observed data, given that the null hypothesis is true.

     

  4. The p-value is, in future experiments, the probability of obtaining results as "extreme" or more "extreme" given that the null hypothesis is true.

     

  5. The p-value is a convenient test statistic.

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p-values: Take the test!

True or False?

  1. The p-value is the probability that the null hypothesis is true.

     

  2. The p-value is The probability that the alternative hypothesis is true.

     

  3. The p-value is the likelihood of the observed data, given that the null hypothesis is true.

     

  4. The p-value is, in future experiments, the probability of obtaining results as "extreme" or more "extreme" given that the null hypothesis is true.

     

  5. The p-value is a convenient test statistic.

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Properties of "p-values"

The Good
Tend to be small when the alternative hypothesis is true. Easier to digest than "t-statistics".
The Bad
Inadequate as data summary, without more information, ie. the sample size, mean difference, standard error, etc.
The Ugly
Oversized studies lead to "significant" p-values with tiny alternatives. Undersized studies lead to "non-significant" p-values with large alternatives.
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Drawing Conclusions About a Proportion

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Other Web Stuff

 

The X10 Project

http://www.dartmouth.edu/~matc/X10/X10.html