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Luis A. Afonso
Posts:
4,725
From:
LIsbon (Portugal)
Registered:
2/16/05


A rarely shown fact about pvalues
Posted:
Mar 29, 2013 5:11 AM


A rarely shown fact about pvalues
Note that because we are performing a *pointwise* test, H0: mu= mu0, and only with *mu0 data* the pvalues are uniformly distributed, it follows that in real world the probability to observe a *significant* value is effectively larger than alpha when we are dealing with a right onetailed test. In fact the pvalues Distribution is, even slightly, left skewed and we stand at an *at most * alpha level. Preferably they join together near 1.
............................ <real alpha< __________________________________________1.0 ....... Alpha=0.05 __________P ............false positives
By real alpha we note the interval inside which fall the 0.05 proportion of test values concerning the real distribution of pvalues.. Note that from the supposed critical value when the pvalues are uniformly distributed and the [  , 1.0 ] interval containing the alpha proportion of them is the false positive region. They are classified wrongly positive in spite to be situated at the 5% interval [P, 1.0] left bound.
Simulation results
A test statistics is supposed to follow a Normal Standard z, therefore the pvalues are u= phi(z), with mu0=0. When mu=1, 0.5, 0.2 , the fractions concerning u=0.95 (alpha=5%) are 0.254, 0.134, and 0.079 , all larger than 0.05. The false positive amounts to 24.9, 8.9 and 2.9% respectively.
Luis A. Afonso



