Conditional Fisherʹs exact test as a selection criterion for pair-correlation method. Type I and Type II errors

The pair-correlation method (PCM) has been developed recently for discrimination between two variables. PCM can be used to identify the decisive (fundamental, basic) factor from among correlated variables even in cases when all other statistical criteria fail to indicate significant difference. These decisions are needed frequently in QSAR studies and/or chemical model building. The conditional Fisherʹs exact test, based on testing significance in the 2×2 contingency tables is a suitable selection criterion for PCM. The test statistic provides a probabilistic aid for accepting the hypothesis of significant differences between two factors, which are almost equally correlated with the response (dependent variable). Differentiating between factors can lead to alternative models at any arbitrary significance level. The power function of the test statistic has also been deduced theoretically. A similar derivation was undertaken for the description of the influence of Type I (false-positive conclusion, error of the first kind) and Type II (false-negative conclusion, error of the second kind) errors. The appropriate decision is indicated from the low probability levels of both false conclusions.