  In a binary classification problem the feature vector (predictor) is the
input to a scoring function that produces a decision value (score), which is
compared to a particular chosen threshold to provide a final class prediction
(output). Although the normal assumption of the scoring function is important
in many applications, sometimes it is severely violated even under the simple
multinormal assumption of the feature vector. This article proves this result
mathematically with a counter example to provide an advice for practitioners to
avoid blind assumptions of normality. On the other hand, the article provides a
set of experiments that illustrate some of the expected and well-behaved
results of the Area Under the ROC curve (AUC) under the multinormal assumption
of the feature vector. Therefore, the message of the article is not to avoid
the normal assumption of either the input feature vector or the output scoring
function; however, a prudence is needed when adopting either of both.
