Value of p-Value.

The goal of this manuscript is to discuss important aspects of external validation of classification and category Quantitative Structure - Activity/Property/Toxicity Relationship QS/A/P/T/R models that to the best of author's knowledge are not addressed in publications. Statistical significance (in terms of p-value) and accuracy of prediction (in terms of Correct Classification Rate (CCR)) of external validation set compounds are among most important characteristics of the models. We assert that in most cases the models built for classification or category response variable should be statistically significant and predictive for each class or category. We show that three thresholds of the number of compounds in each class or category of the external validation sets should be satisfied. 1) The p-value criterion can never be satisfied, if the number of compounds is below the first threshold. 2) If the number of compounds is between the first and the second thresholds, p-value criterion should be used. 3) If it is higher than the third threshold, classification or category accuracy criterion should be used. 4) If the number of compounds is between second and third thresholds, either one or the other criterion should be used depending on the value of p-value. 5) When the number of compounds in the class approaches infinity, the maximum relative error of prediction approaches the relative expected error. The results are of interest in other areas of multidimensional data analysis.