Non-Central T Distribution
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Description: This demonstration shows how the t distribution changes, that is, it becomes skewed, when the null hypothesis is not true. Note this demonstration is not altogether different from the JMP built-in script, demoAlpha, which plots the theoretical t distribution under the null hypothesis and the alternative hypothesis with a noncentrality parameter. This example may be more compelling, however, because it is empirically derived. This quality may provoke more discussion about the nature of the asymmetry.
Instructions: Open and run the script. Accept the default conditions, which represent the case when the null hypothesis is true, by clicking the OK button. After a delay while JMP samples and computes the sample statistics, a data table appears with the t statistic for each sample and a distribution platform launches for these statistics.
Note the red curve is the t distribution for the null case.
Note the platform window is completely interactive after the script finishes.
Now run the script again but this time change the first parameter, population mean, to 1, which represents a shift in the mean equal to 1 standard deviation, and then click OK. Note the red curve is unchanged but the sample t statistics are now shifted and skewed to the right.
Note you can simulate any population approximated by a Gaussian distribution and any test of the mean.
For example, you might expect 12 amperes from a particular model of a power supply and a 0.25 amp standard deviation in the population of power supplies, but the current actually dropped to 11 amperes. You run a test of 25 units. This situation is easily simulated by entering in the opening dialog, in order, 11, 0.25, 12, 25, and 1000.
Requirements: None
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