Can I do a correlation between two variables where one variable is always less than or equal to the other?
Yes you can because this doesn't constrain the value of the correlation.
Consider the two examples below both of which have one variable (x say) less than the other (y). The first has a near zero correlation (Kendall = -.067) whereas the second has a perfect correlation of 1. The reason for this is just because x is less than or equal to y it doesn't tell you how much lower (if at all) x is than y. If x is always a fixed constant amount lower than y you have perfect correlation (in the second example below x is always 1 lower than y).
Family Size |
Family Size Estimate |
1 |
4 |
2 |
12 |
3 |
43 |
4 |
23 |
5 |
11 |
6 |
9 |
x |
y |
1 |
2 |
2 |
3 |
3 |
4 |
4 |
5 |
5 |
6 |
6 |
7 |