Joint Distribution Tables

# get the pipe operator
library(magrittr)

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

str(HairEyeColor)

##  table [1:4, 1:4, 1:2] 32 53 10 3 11 50 10 30 10 25 ...
##  - attr(*, "dimnames")=List of 3
##   ..$ Hair: chr [1:4] "Black" "Brown" "Red" "Blond"
##   ..$ Eye : chr [1:4] "Brown" "Blue" "Hazel" "Green"
##   ..$ Sex : chr [1:2] "Male" "Female"

Sum across sex:

HairEyeColor %>% 
  margin.table(c(1,2))

##        Eye
## Hair    Brown Blue Hazel Green
##   Black    68   20    15     5
##   Brown   119   84    54    29
##   Red      26   17    14    14
##   Blond     7   94    10    16

Joint distribution table (combined across gender):

HairEyeColor %>% 
  margin.table(c(1,2)) %>% 
  prop.table() %>% 
  round(2)

##        Eye
## Hair    Brown Blue Hazel Green
##   Black  0.11 0.03  0.03  0.01
##   Brown  0.20 0.14  0.09  0.05
##   Red    0.04 0.03  0.02  0.02
##   Blond  0.01 0.16  0.02  0.03

Marginal for hair:

HairEyeColor %>% 
  margin.table(1) %>% 
  prop.table() %>% 
  round(2)

## Hair
## Black Brown   Red Blond 
##  0.18  0.48  0.12  0.21

Marginal for eye:

HairEyeColor %>% 
  margin.table(2) %>% 
  prop.table() %>% 
  round(2)

## Eye
## Brown  Blue Hazel Green 
##  0.37  0.36  0.16  0.11

Conditional distribution given eye:

HairEyeColor %>% 
  margin.table(c(1,2)) %>% 
  prop.table(2) %>% 
  round(2)

##        Eye
## Hair    Brown Blue Hazel Green
##   Black  0.31 0.09  0.16  0.08
##   Brown  0.54 0.39  0.58  0.45
##   Red    0.12 0.08  0.15  0.22
##   Blond  0.03 0.44  0.11  0.25

Conditional distribution given hair:

HairEyeColor %>% 
  margin.table(c(1,2)) %>% 
  prop.table(1) %>% 
  round(2)

##        Eye
## Hair    Brown Blue Hazel Green
##   Black  0.63 0.19  0.14  0.05
##   Brown  0.42 0.29  0.19  0.10
##   Red    0.37 0.24  0.20  0.20
##   Blond  0.06 0.74  0.08  0.13