Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

p-Values Are Random Variables

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

We consider -values for or simulations using a random sample of size from a normal distribution with mean and unit variance to compute the two-sided -values for the test of the null hypothesis, versus using the -distribution method as implemented in the Mathematica function MeanTest. When , the -values are uniformly distributed on . With simulations, the result is obtained very quickly but there is more random variability in the histogram. Increasing to simulations takes less than three seconds on most modern computers and provides a more accurate result.

[more]

Mouseover the first rectangle to see the estimate of the probability of the power of a 5% test; the area of this rectangle represents observed probability of -values in the interval .

The slider changes the alternate hypothesis. When , the -values are no longer uniform on . The area under the first rectangle gives an estimate of the probability that the -value is less than 0.05. This is the estimated power of a two-sided test at the 5% level for

The distribution of the -values may also be visualized using a Q-Q plot in which the quantiles of the -values are plots against the corresponding quantiles from a uniform distribution.

[less]

Contributed by: Ian McLeod (University of Western Ontario) (March 2011)
Open content licensed under CC BY-NC-SA

Snapshots

Details

-values are defined as the probability of observing a value as extreme or more extreme than the observed if the null hypothesis is true. Beginning students often do not realize that -values, just like confidence intervals, are random in repeated sampling and this point is often not discussed in elementary textbooks, as noted in [1].

For more on the Q-Q plot see [2].

[1] D. J. Murdoch, Y.-L. Tsai, and J. Adcock, "P‐Values Are Random Variables," The American Statistician, 62(3), 2008 pp. 242–245.

[2] W. S. Cleveland, Visualizing Data, Summit, NJ: Hobart Press, 1993.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send