P Values
P Values. Photo by Charles Hoffman

A p-value is used to decide whether hypothesis test results are statistically significant or not. Once a p-value is calculated from analyzing test data, it is compared to the selected alpha level – if lower than the alpha level, the results are deemed to be statistically significant; if higher, the results are deemed to not be statistically significant.

A p-value is expressed as a number between 0 and 1.

This Khan Academy video explains p-values, and how they apply to hypothesis tests, in-depth:

While the p-value is a standard method of determining this key measurement of one’s results, there are a mix of opinions on whether it’s actually the ideal solution.

Geoff Cumming—Emeritus Professor at La Trobe University in Melbourne, Australia—explains his distrust of p-values in hypothesis testing in this video:

But then, Jeff Leek and Rafa Irizarry disagree, and their article lists a number of useful properties of the p-value. To summarize (the full list, with explanations, is available in the linked article):

  • They’re easy to calculate.
  • They’re easy to understand.
  • They have simple, universal properties.
  • Their calibration is within useful error rates.
  • They can be used in correction of multiple tests.
  • They’re reproducible.

Further Information About P-Values

What is the difference between an alpha level and a p-value? (PDF)

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