Table 4.
Alphabet size and performance.
| (A) Tetrapod Myoglobin | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Method | A1 | A2 | A3 | A4 | A5 | |||||
| τ | p-value | τ | p-value | τ | p-value | τ | p-value | τ | p-value | |
| MI | -0.20 | 4.8 × 10-1 | 0.42 | 1.1 × 10-1 | 0.16 | 6.0 × 10-1 | -0.33 | 2.2 × 10-1 | 0.24 | 3.8 × 10-1 |
| NMI | -0.29 | 2.9 × 10-1 | 0.24 | 3.8 × 10-1 | 0.24 | 3.8 × 10-1 | 0.16 | 6.0 × 10-1 | 0.56 | 2.9 × 10-3 |
| RMI | 0.11 | 7.3 × 10-1 | 0.33 | 2.2 × 10-1 | -0.51 | 4.7 × 10-3 | -0.02 | 1.0 | 0.64 | 9.1 × 10-3 |
| SCA8 | -0.24 | 3.8 × 10-1 | 0.78 | 9.5 × 10-34* | 0.56 | 2.9 × 10-3 | -0.02 | 1.0 | 0.87 | 1.2 × 10-34* |
| MIp | 0.16 | 6.0 × 10-1 | 0.47 | 7.3 × 10-2 | 0.29 | 2.9 × 10-1 | -0.11 | 7.3 × 10-1 | 0.78 | 9.5 × 10-34 * |
| AS | -0.02 | 1.0 | 0.64 | 9.1 × 10-3 | 0.29 | 2.9 × 10-1 | -0.47 | 7.3 × 10-2 | 0.07 | 8.6 × 10-1 |
| G7 | 0.16 | 6.0 × 10-1 | 0.64 | 9.1 × 10-3 | 0.33 | 2.2 × 10-1 | 0.42 | 1.1 × 10-1 | 0.47 | 7.3 × 10-2 |
| (B) Randomized Tetrapod Myoglobin | ||||||||||
| Method | A1 | A2 | A3 | A4 | A5 | |||||
| τ | p-value | τ | p-value | τ | p-value | τ | p-value | τ | p-value | |
| MI | -0.38 | 1.6 × 10-1 | -0.29 | 2.9 × 10-1 | -0.07 | 8.6 × 10-1 | 0.16 | 6.0 × 10-1 | 0.60 | 1.7 × 10-3 |
| NMI | -0.29 | 2.9 × 10-1 | -0.16 | 6.0 × 10-1 | -0.47 | 7.3 × 10-2 | -0.07 | 8.6 × 10-1 | 0.16 | 6.0 × 10-1 |
| RMI | -0.38 | 1.6 × 10-1 | -0.29 | 2.9 × 10-1 | -0.11 | 7.3 × 10-1 | -0.16 | 6.0 × 10-1 | 0.56 | 2.9 × 10-3 |
| SCA8 | -0.73 | 2 2 × 10-3 | -0.69 | 4.7 × 10-3 | -0.60 | 1.7 × 10-3 | -0.64 | 9.1 × 10-3 | 0.07 | 8.6 × 10-1 |
| MIp | -0.38 | 1.6 × 10-1 | -0.69 | 4.7 × 10-3 | -0.42 | 1.1 × 10-1 | -0.11 | 7.3 × 10-1 | 0.29 | 2.9 × 10-1 |
| AS | -0.56 | 2.9 × 10-3 | -0.42 | 1.1 × 10-1 | -0.38 | 1.6 × 10-1 | -0.38 | 1.6 × 10-1 | -0.24 | 3.8 × 10-1 |
| G7 | 0.60 | 1.7 × 10-3 | 0.29 | 2.9 × 10-1 | -0.29 | 2.9 × 10-1 | 0.56 | 2.9 × 10-3 | 0.20 | 4.8 × 10-1 |
| (C) Chordate Myosin | ||||||||||
| Method | A1 | A2 | A3 | A4 | A5 | |||||
| τ | p-value | τ | p-value | τ | p-value | τ | p-value | τ | p-value | |
| MI | 0.78 | 9.5 × 10-34* | 0.78 | 9.5 × 10-34* | 0.64 | 9.1 × 10-3 | 0.60 | 1.7 × 10-3 | 0.82 | 3.6 × 10-34* |
| NMI | 0.69 | 4.7 × 10-3 | 0.78 | 9.5 × 10-34* | 0.56 | 2.9 × 10-3 | 0.29 | 2.9 × 10-1 | 0.82 | 3.6 × 10-34* |
| RMI | 0.29 | 2.9 × 10-1 | 0.29 | 2.9 × 10-1 | -0.07 | 8.6 × 10-1 | -0.51 | 4.7 × 10-3 | 0.60 | 1.7 × 10-3 |
| SCA6 | 0.56 | 2.9 × 10-3 | 0.20 | 4.8 × 10-1 | 0.16 | 6.0 × 10-1 | -0.07 | 8.6 × 10-1 | 0.16 | 6.0 × 10-1 |
| MIp | 0.78 | 9.5 × 10-34* | 0.78 | 9.5 × 10-34* | 0.69 | 4:7 × 10-3 | 0.60 | 1.7 × 10-3 | 0.73 | 2.2 × 10-3 |
| AS | -0.16 | 6.0 × 10-1 | 0.29 | 2.9 × 10-1 | 0.73 | 2:2 × 10-3 | 0.42 | 1.1 × 10-1 | 0.29 | 2.9 × 10-1 |
| (D) Randomized Chordate Myosin | ||||||||||
| Method | A1 | A2 | A3 | A4 | A5 | |||||
| τ | p-value | τ | p-value | τ | p-value | τ | p-value | τ | p-value | |
| MI | -0.51 | 4.7 × 10-3 | -0.33 | 2.2 × 10-1 | -0.07 | 8.6 × 10-1 | 0.16 | 6.0 × 10-1 | -0.16 | 6.0 × 10-1 |
| NMI | -0.20 | 4.8 × 10-1 | -0.78 | 9.5 × 10-34* | -0.29 | 2.9 × 10-1 | 0.51 | 4.7 × 10-3 | 0.20 | 4.8 × 10-1 |
| RMI | -0.33 | 2.2 × 10-1 | -0.60 | 1.7 × 10-3 | -0.24 | 3.8 × 10-1 | 0.16 | 6.0 × 10-1 | -0.11 | 7.3 × 10-1 |
| SCA6 | -0.16 | 6.0 × 10-1 | -0.56 | 2.9 × 10-3 | -0.60 | 1.7 × 10-3 | 0.20 | 4.8 × 10-1 | -0.24 | 3.8 × 10-1 |
| MIp | -0.29 | 2.9 × 10-1 | -0.47 | 7.3 × 10-2 | -0.64 | 9.1 × 10-3 | 0.38 | 1.6 × 10-1 | -0.51 | 4.7 × 10-3 |
| AS | 0.20 | 4.8 × 10-1 | 0.20 | 4.8 × 10-1 | -0.11 | 7.3 × 10-1 | 0.02 | 1.0 | -0.11 | 7.3 × 10-1 |
For each of the five heuristically defined alphabets, Kendall correlation coefficients (τ) and corresponding p-values are provided to illustrate the relationship between performance rank and alphabet size. Bolded values highlight p-values = 0.05, and starred values indicated p-values significant after adjustment for multiple comparisons (A-B Bonferroni-adjusted α = 0.0014, C-D Bonferroni-adjusted α = 0.0017). Tau range: [-1., 1.]. A positive τ value indicates a positive correlation (i.e., increased alphabet size is associated with increased performance), and a negative τ value indicates a negative correlation (i.e., decreased alphabet size is associated with increased performance).