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Let T be a test statistic with a continuous and monotone probability distribution function Fo(t) := P(T≤t) under Ho. Then 1 - Fo(t) is the p-value of the test that rejects Ho for large values of t. (a) (b) Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1]. Suppose now that you are not a fair scientist, so that you perform each experiment twice and you report just the highest p-value of each couple of measurements. Which is in this case the distribution of the reported p-values under Ho?

Let T be a test statistic with a continuous and monotone probability distribution function Fo(t) := P(T≤t) under Ho. Then 1 - Fo(t) is the p-value of the test that rejects Ho for large values of t. (a) (b) Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1]. Suppose now that you are not a fair scientist, so that you perform each experiment twice and you report just the highest p-value of each couple of measurements. Which is in this case the distribution of the reported p-values under Ho?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let T be a test statistic with P(T≤t) under Ho. Then 1- a continuous and monotone probability distribution function Fo(t) = Fo(t) is the p-value of the test that rejects Ho for large values of t. Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1]. Suppose now that you are not a fair scientist, so that you perform each experiment twice and you report just the highest p-value of each couple of measurements. Which is in this case the distribution of the reported p-values under Ho?
Transcribed Image Text:Let T be a test statistic with P(T≤t) under Ho. Then 1- a continuous and monotone probability distribution function Fo(t) = Fo(t) is the p-value of the test that rejects Ho for large values of t. Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1]. Suppose now that you are not a fair scientist, so that you perform each experiment twice and you report just the highest p-value of each couple of measurements. Which is in this case the distribution of the reported p-values under Ho?
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