# Ranks
# Dennis E. Slice (c) 2012
# Show relationships between values and ranks

# Sweep the deck
rm(list=ls())

# Set sample size, et al.
n = 100
par(ask=T)

# Some independent (r=0) variables.
y1 = rnorm(100)
y2 = rnorm(100)

plot(y1,y2)
y1.rank = rank(y1)
y2.rank = rank(y2)
print(y1.rank)
print(y2.rank)
plot(y1.rank,y2.rank)

# Now some correlated variables
r = -0.8
y1 = rnorm(n)
y.hold = rnorm(n)
y2 = y1*r + (1-r*r)*y.hold
plot(y1,y2)
y1.rank = rank(y1)
y2.rank = rank(y2)
print(y1.rank)
print(y2.rank)
plot(y1.rank,y2.rank)

# Pause until Return to continue
print("Press Return to continue...")
readline()

# Pearson v. Spearman
pearsons.r = cor.test(y1,y2)
print(pearsons.r)
spearmans.rho = cor.test(y1,y2,method="s")
print(spearmans.rho)
print(cor.test(rank(y1),rank(y2)))

# Pause until Return to continue
print("Press Return to continue...")
readline()

# And Kendall's tau
kendalls.tau = cor.test(y1,y2,method="k")
print(kendalls.tau)

# Again, with less correlation
r = 0.3
y1 = rnorm(n)
y.hold = rnorm(n)
y2 = y1*r + (1-r*r)*y.hold

# Pearson v. Spearman v. Kendall
pearsons.r = cor.test(y1,y2)
print(pearsons.r)
spearmans.rho = cor.test(y1,y2,method="s")
print(spearmans.rho)
print(cor.test(rank(y1),rank(y2)))
kendalls.tau = cor.test(y1,y2,method="k")
print(kendalls.tau)