# Data:  Eight daily temperatures (degrees C) at a South Florida weather station
# and at an experimental pasture site.  Of interest is whether the median difference is zero.

# Source:  Rao (1998), p. 187.

weather <- c(34.5,35.4,35.9,33.4,36.9,35.8,36.0,37.4)
pasture <- c(33.2,32.9,33.4,32.3,34.1,33.0,33.3,34.6)

# Let differences = weather - pasture:

diffs <- weather - pasture

hist(diffs)
# Histogram

qqnorm(diffs)
# Q-Q plot shows non-normality

wilcox.test(diffs, alternative="two.sided", mu=0)

# The Wilcoxon Signed Rank test on the differences concludes 
# (at significance level .05) that the true median difference is not 0.
# P-value given as 0.01368.

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

# What if we had been testing whether the true median difference 
# was GREATER than 0 (i.e., weather station temperatures higher)?

wilcox.test(diffs, alternative="greater", mu=0)

# The Wilcoxon Signed Rank test on the differences concludes 
# (at significance level .05) that the true median difference is greater than 0.
# P-value given as 0.0068.