Resumen
This note focuses on the relationship between Spearman's ?n and Kendall's ?n for the two extreme order statistics X(1) and X(n) of n independent and identically distributed continuous random variables. We present three new formulas for computing Spearman's ?n. One of the formulas leads to a recursion relation. We use this recursion relation to establish inequality relationships between ?n and ?n. The recursion relation also provides an alternative proof of the result that the sequence of ratios ?n/?n converges to 32 as the sample size n goes to infinity.

Resumen
The power of a statistical test depends on the sample size. Moreover, in a randomized trial where two treatments are compared, the power also depends on the number of assignments of each treatment. We can treat the power as the conditional probability of correctly detecting a treatment effect given a particular treatment allocation status. This paper uses a simple z-test and a t-test to demonstrate and analyze the power function under the biased coin design proposed by Efron in 1971. We numerically show that Efron's biased coin design is uniformly more powerful than the perfect simple randomization.