Table 1. The median sample size for each method to achieve power 85% at type one error level 0.05, grouped into monotone (type 1–5) and non-monotone relationships (type 6–19) for both one- and ten-dimensional settings, normalized by the number of samples required by Mgc.
In other words, a 2.0 indicates that the method requires double the sample size to achieve 85% power relative to Mgc. Pearson, Rv, and Cca all achieve the same performance, as do Spearman and Kendall. Mgc requires the fewest number of samples in all settings, and for high-dimensional non-monotonic relationships, all other methods require about double or triple the number of samples Mgc requires.
Table 1—source data 1. Testing power sample size data in one dimension.
elife-41690-table1-data1.mat (6.4KB, mat)
DOI: 10.7554/eLife.41690.010
Table 1—source data 2. Testing power sample size data in high-dimensions.
elife-41690-table1-data2.mat (6KB, mat)
DOI: 10.7554/eLife.41690.011
| Dimensionality | One-Dimensional | Ten-Dimensional | ||||
|---|---|---|---|---|---|---|
| Dependency type | Monotone | Non-Mono | Average | Monotone | Non-Mono | Average |
| Mgc | 1 | 1 | 1 | 1 | 1 | 1 |
| Dcorr | 1 | 2.6 | 2.2 | 1 | 3.2 | 2.6 |
| Mcorr | 1 | 2.8 | 2.4 | 1 | 3.1 | 2.6 |
| Hhg | 1.4 | 1 | 1.1 | 1.7 | 1.9 | 1.8 |
| Hsic | 1.4 | 1.1 | 1.2 | 1.7 | 2.4 | 2.2 |
| Mantel | 1.4 | 1.8 | 1.7 | 3 | 1.6 | 1.9 |
| Pearson / Rv / Cca | 1 | >10 | >10 | 0.8 | >10 | >10 |
| Spearman / Kendall | 1 | >10 | >10 | n/a | n/a | n/a |
| Mic | 2.4 | 2 | 2.1 | n/a | n/a | n/a |