Figure 6.

Separation of a largest value from the others and the basic measures for the Dixon test. This diagram displays the separation of a largest value from the others when the values being compared are sorted from smallest to largest, x_i − 1 ⩽ x_i. The separation ratio τ, is the distance between the largest and the next-to-largest values (gap = x_n − x_n − 1) divided by the distance between the largest and smallest values (x_n − x₁). The ratio τ is fundamental in the Dixon test for discordancy (Barnett and Lewis 1978a), which assesses statistically how exceptionally large the largest value is compared to the others. See equations 1–6 in Algorithm Details. In the examples, f_max = 1.