Example R programs and commands
		 10. Homoscedasticity vs heteroscedasticity

# All lines preceded by the "#" character are my comments.
# All other left-justified lines are my input.
# All other indented lines are the R program output.
#
# Tabulated data for input to R
# 
#    ORIGINAL FORMAT
#  
#    X1      X2     X3
#   ---     ---    ---
#   6.9     8.8    1.3
#   7.7     7.5    1.9
#   5.9     8.0    1.8
#   9.6     8.1    2.2
#   7.8     7.0    1.8
#   3.6     8.2    2.1

x1 <- c( 6.9, 7.7, 5.9, 9.6, 7.8, 3.6)
x2 <- c( 8.8, 7.5, 8.0, 8.1, 7.0, 8.2)
x3 <- c( 1.3, 1.9, 1.8, 2.2, 1.8, 2.1)
x <- gl(3,6) # default labels 1,2,3; equal replications (6) per level
y <- c(x1,x2,x3)

# Bartlett's test of homoscedasticity:
bartlett.test(y,x)

        Bartlett test of homogeneity of variances

   data:  y and x
   Bartlett's K-squared = 14.4326, df = 2, p-value = 0.0007345

# ... large statistic implies low p-value implies REJECT H_0
# Formula notation gives the same result:
bartlett.test(y~x)

        Bartlett test of homogeneity of variances

   data:  y by x
   Bartlett's K-squared = 14.4326, df = 2, p-value = 0.0007345


# Nonparametric alternative to Bartlett is called Fligner's test:
fligner.test(y~x)

        Fligner-Killeen test of homogeneity of variances

   data:  y by x
   Fligner-Killeen:med chi-squared = 6.2885, df = 2, p-value = 0.0431