Dipartimento di Scienze Statistiche

In this paper we use the test on the difference between proportions, in discrete field, to trait the conditioned and absolute significance and to give some reflection about a logic reversal of the hypothesis testing. In order to discuss sample representativeness an experimental model is formulated. The work aims to propose a test to asses whether two samples with respective proportions p1 and p 2 come from the same dicothomous population with given parameter p greek (state of Nature), assessed or proposed by the researcher. The discussion of the subsequent topics is focused on p greek . The problem is formulated as hypothesis test, then we discuss the test statistic and some critical remarks on the Normal approximation, based on skewness index and kurtosis. The procedure gives the sample distributions under binomial and hypergeometric distributions. Tables are presented to illustrate the variability of the critical values when p greek and the sample size vary. The procedure has been implemented into a software (DPT.exe) that can be requested to and freely provided by the Author. This work has an operational function because it uses the application DPT and given the detailed processing phases carried out and described by the software, it is also a valuable didactical instrument. The work brings together the contents of a previous Rapporto Tecnico n. 11, Maggio 2007, DSPSA, La Sapienza, Roma, and some additional considerations relating to Sections 3.2, 4.1 and 4.2 ready in June 2008, and that was not possible to publish before.