## Section 5.4 examples

## MBA Example:

gmat <- c(710,610,640,580,545,560,610,530,560,540,570,560)
gpa <- c(4.0,4.0,3.9,3.8,3.7,3.6,3.5,3.5,3.5,3.3,3.2,3.2)

### Spearman's rho:

cor.test(gmat, gpa, alternative="greater", method="spearman", exact=T)

## Note that the Spearman coefficient is the same as the Pearson coefficient
## calculated on the ranks of each sample:

cor(gmat, gpa, method="spearman")
cor(rank(gmat), rank(gpa), method="pearson")


### Kendall's tau:

cor.test(gmat, gpa, alternative="greater", method="kendall", exact=T)

##############################

## Daniels Test for Trend:

global.temps <- c(-0.493, -0.457, -0.466, -0.497, -0.315, -0.077, 0.063, -0.036, -0.025, -0.002, 0.317, 0.563, 0.923)

time <- 1:length(global.temps)

# Using Spearman:

cor.test(time, global.temps, alternative="greater", method="spearman", exact=T)

# Using Kendall:

cor.test(time, global.temps, alternative="greater", method="kendall", exact=T)


#################################

### Kendall's Tau for binary ordered data:

math    <- c(0,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,1,1,1,1)
history <- c(0,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1)

cor.test(math, history, alternative="two.sided", method="kendall", exact=T)