Question

The dataset HairEyesColor in R contains classifications of students by gender, color, and eye color.

a) How many students are included in the data set?

b) Display the information using mosaicplot (HairEyeColor, col=c(1,2))

c) Is hair color independent of eye color for men?

d) Is hair color independent of eye color for women?

Use R and show R code

Answer 1

The R code is as follows

require(graphics)
data("HairEyeColor")
HairEyeColor

sum(HairEyeColor)
## Full mosaic
mosaicplot(HairEyeColor)
## Aggregate over sex (as in Snee's original data)
x <- apply(HairEyeColor, c(1, 2), sum)
x
mosaicplot(x, main = "Relation between hair and eye color")

# Mosaic Plot using VCD
library(vcd)
mosaic(HairEyeColor, shade=TRUE, legend=TRUE,main = "Relation between hair and eye color")

The results are

HairEyeColor
, , Sex = Male

Eye
Hair Brown Blue Hazel Green
Black 32 11 10 3
Brown 53 50 25 15
Red 10 10 7 7
Blond 3 30 5 8

, , Sex = Female

Eye
Hair Brown Blue Hazel Green
Black 36 9 5 2
Brown 66 34 29 14
Red 16 7 7 7
Blond 4 64 5 8

> sum(HairEyeColor)
[1] 592

The colors represent the level of the residual for that cell / combination of levels. The legend is presented at the plot's right. More specifically, blue means there are more observations in that cell than would be expected under the null model (independence). Red means there are fewer observations than would have been expected.

we see that the values are signficant for all hair colors within the male and female combinations , hence there is a relationship

read 2 rows from the graph at a time