On the Correct Use of Statistical Tests: Reply to "Lies, damned lies and statistics (in Geology)"

In a Forum published in EOS Transactions AGU (2009) entitled "Lies, damned lies and statistics (in Geology)", Vermeesch (2009) claims that "statistical significant is not the same as geological significant", in other words, statistical tests may be misleading. In complete contradiction, we affirm that statistical tests are always informative. We detail the several mistakes of Vermeesch in his initial paper and in his comments to our reply. The present text is developed in the hope that it can serve as an illuminating pedagogical exercise for students and lecturers to learn more about the subtleties, richness and power of the science of statistics.