Generalized p-value: Difference between revisions

Revision as of 22:58, 20 December 2011

Revision as of 14:19, 18 May 2012

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:<math>R = \frac {\overline{x} S} {s \sigma} - \frac{\overline{X}- \mu} {\sigma}

= \frac {\overline{x}} {s} \frac {\sqrt{U}} {\sqrt{n}} ~-~ \frac {Z} {\sqrt{n}} ,</math>

where <math>\overline{x}</math> is the observed value of <math>\overline{X}</math> and <math>s</math> is the observed value of <math>S</math>. Note that the distribution of <math>R</math> and its observed value are both free of nuisance parameters. Therefore, a test of a hypothesis with a one-sided alternative such as <math> H_A : \rho <\lt \rho_0 </math> can be based on the generalized p-value <math> p = Pr( R \ge \rho_0 )</math>, a quantity that can be evaluated via Monte Carlo simulation or using the non-central t-distribution.

==Notes==