In the absence of ties the statistic t is based on the ranks of the X observations and Y observations. It is clear from the definition of t that if the ranks of the X observations and Y observations...

In the absence of ties the statistic t is based on the ranks of

the X observations and Y observations. It is clear from the

definition of t that if the ranks of the X observations and Y

observations replace the observations themselves, the value of

t is not altered.

(a) Use the 24 possible permutations of the Y ranks together

with the X ranks 1, 2, 3, 4 to find the null distribution

of t for n = 4.

(b) Verify th!¢ E(t) 0 and Var(t) (4/9)(n + 5/2)/n(n - 1),

in this case.