# Data:  Dental measurements (in mm) for two groups:  
# a group of 16-year-old females and another group of 16-year-old males
# Of interest is whether the median of the male population is greater than the 
# median of the female population.

# Source:  Rao (1998), p. 147.

girls <- c(23,25.5,26,26.5,23.5,22.5,25,24,21.5,19.5,28)
boys <- c(31,26.5,27.5,27,26,28.5,26.5,25.5,26,31.5,25,28,29.5,26,30,25)



hist(boys)

hist(girls)
# Histograms

qqnorm(boys)

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

boxplot(boys, girls)
# Do spreads for the two groups look roughly equal?


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

# We are testing whether the true median of boys is greater than
# that of girls, so we list boys first, and then the "greater" alternative

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

# The Wilcoxon Rank Sum test concludes 
# (at significance level .05) that the true median for boys 
# is greater than the median for girls.
# P-value given as 0.001.