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