Figure 1

Permutation-based analyses. Alon's colon cancer data (left) and Singh's prostate cancer data (right). Boxplots of the minimal error rates , and for the 20 permutations, and of all the error rates obtained with the 124 classifiers for the 20 permutations = 124 × 20 points (right). The three horizontal lines represent the three baseline error rates defined as follows: the error rate obtained by assigning all observations to the majoritary class (plain), the error rate obtained by randomly assigning N ₀ observations to class 0 and N ₁ observations to class 1 (dotted), and 50% (dashed). Main conclusion: The minimal error rate is much lower than all three baseline error rates, and a large part of this bias is due to the optimal selection of the classification method.