Table 1.
Empirical size and power 
of the tests based on projection correlation, ranks of distances and distance correlation for different 
in Example 1 with 
and
. All numbers reported in this table are multiplied by
| Scenario |
|
Test |
|
|
|
|
|
|
|---|---|---|---|---|---|---|---|---|
| (1a) |
|
Projection correlation | 1·1 | 28·4 | 53·4 | 70·0 | 80·1 | 88·1 |
| Ranks of distances | 0·9 | 2·7 | 8·1 | 20·1 | 36·2 | 52·3 | ||
| Distance correlation | 1·3 | 2·9 | 3·4 | 4·1 | 4·2 | 4·4 | ||
|
Projection correlation | 4·9 | 52·9 | 75·1 | 87·7 | 93·0 | 96·0 | |
| Ranks of distances | 4·9 | 11·2 | 25·1 | 42·2 | 60·4 | 75·2 | ||
| Distance correlation | 6·1 | 5·3 | 5·4 | 6·3 | 6·4 | 6·1 | ||
| (1b) |
|
Projection correlation | 1·2 | 20·8 | 41·7 | 61·5 | 76·3 | 84·8 |
| Ranks of distances | 0·9 | 2·3 | 8·0 | 19·5 | 35·3 | 51·3 | ||
| Distance correlation | 1·4 | 3·0 | 4·0 | 4·2 | 4·5 | 5·0 | ||
|
Projection correlation | 5·2 | 39·9 | 64·8 | 81·4 | 89·5 | 94·6 | |
| Ranks of distances | 5·2 | 8·3 | 21·1 | 38·8 | 60·4 | 76·1 | ||
| Distance correlation | 4·5 | 4·8 | 5·9 | 5·3 | 5·9 | 6·6 | ||
| (1c) |
|
Projection correlation | 1·0 | 65·1 | 98·8 | 100 | 100 | 100 |
| Ranks of distances | 0·9 | 20·3 | 58·9 | 87·1 | 96·6 | 99·5 | ||
| Distance correlation | 0·9 | 67·0 | 98·3 | 100 | 100 | 100 | ||
|
Projection correlation | 4·5 | 82·0 | 99·6 | 100 | 100 | 100 | |
| Ranks of distances | 4·7 | 37·7 | 79·6 | 96·2 | 99·1 | 100 | ||
| Distance correlation | 5·1 | 82·3 | 99·5 | 100 | 100 | 100 |