Caracterización de la distribución de los valores p de las pruebas paramétricas en poblaciones normales

Hypothesis test are widely used in data analysis but, in general, the random nature of p value is not consider in such applications. Power function and p-value probability distribution are strongly related, this relationship should be a component in both hypothesis testing conclusions and sample size calculation. However, this is not the case, possibly due of to two factors: first many people ignore the random nature of p-value and second there is a lack of information in the subject. Some papers introduced some characteristics of p-value distribution as mean value and median, but such values were not obtained for every parametric test in normal populations. This paper contains a full characterization of p-values probability distribution for both one and two sided hypothesis test for parameters in one or two normal populations. P-value probability distribution and their percentiles are presented, emphasizing in median value. Additionally the paper introduces approximate criteria for calculating both distribution function and percentiles, and highlight the relationship between power function and p-value.