The Way of Pooling p-values
Fausto Galetto · Mathematics and Statistics · 2020
Pooling p-values arises both in practical (in any science and engineering applications) and theoretical (statistical) issues. The p-value (sometimes p value) is a probability used as a statistical decision quantity: in practical applications, it is used to decide if an experimenter has to believe that his/her collected data confirm or disconfirm his/her hypothesis about the “reality” of a phenomenon. It is a real number, determination of a Random Variable, uniformly distributed, related to the data provided by the measurement of a phenomenon. Almost all statistical software provides p-values when statistical hypotheses are considered, e.g. in Analysis of Variance and regression methods. Combining the p-values from various samples is crucial, because the number of degrees of freedom (df) of the samples we want to combine is influencing our decision: forgetting this can have dangerous consequences. One way of pooling p-values is provided by a formula of Fisher; unfortunately, this method does not consider the number of degrees of freedom. We will show other ways of doing that and we will prove that theory is more important than any formula which does not consider the phenomenon on which we have to decide: the distribution of the Random Variables is fundamental in order to pool data from various samples. Manager, professors and scholars should remember Deming’s profound knowledge and Juran’s ideas; profound knowledge means “understanding variation (type of variation)” in any process, production or managerial; not understanding variation causes cost of poor quality (more than 80% of sales value) and do not permits a real improvement.