Hypothesis testing is a well-known procedure for data analysis widely used in scientific papers but, at the same time, strongly criticized and its use questioned and restricted in some cases due to inconsistencies observed from their application. This issue is analyzed in this paper on the basis of the fundamentals of the statistical methodology and the different approaches that have been historically developed to solve the problem of statistical hypothesis analysis highlighting a not well known point: the P value is a random variable. The fundamentals of Fisher´s, Neyman-Pearson´s and Bayesian´s solutions are analyzed and based on them, the inconsistency of the commonly used procedure of determining a p value, compare it to a type I error value (usually 0.05) and get a conclusion is discussed and, on their basis, inconsistencies of the data analysis procedure are identified, procedure consisting in the identification of a P value, the comparison of the P-value with a type-I error value –which
is usually considered to be 0.05– and upon this the decision on the conclusions of the analysis. Additionally, recommendations on the
best way to proceed when solving a problem are presented, as well as the methodological and teaching challenges to be faced when analyzing correctly the data and determining the validity of the hypotheses.
Key words: Neyman-Pearson’s hypothesis tests, Fisher’s significance tests, Bayesian hypothesis tests, Vancouver norms, P-value, null-hypothesis.