Load the dataset (it’s built into R)

data(HairEyeColor)

View the dataset structure

str(HairEyeColor)
 'table' num [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"

View the entire dataset

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

Summary statistics

summary(HairEyeColor)
Number of cases in table: 592 
Number of factors: 3 
Test for independence of all factors:
    Chisq = 164.92, df = 24, p-value = 5.321e-23
    Chi-squared approximation may be incorrect

interpretation

Null Hypothesis (H₀): The three factors (hair color, eye color, and sex) are independent of each other

Meaning: Hair color doesn’t affect eye color, sex doesn’t affect hair/eye color combinations, etc.

Alternative Hypothesis (H₁): The factors are NOT independent (they are associated)

Chi-square statistic (164.92):

This measures how much the observed counts differ from what we’d expect if the factors were independent

Larger values indicate stronger evidence against independence

Degrees of freedom (24):

Calculated as: (4 hair colors - 1) × (4 eye colors - 1) × (2 sexes - 1) = 3 × 3 × 1 = 24

This represents the number of “free” pieces of information in the analysis

Extremely small p-value (5.321 × 10⁻²³):

This is 0.0000000000000000000005321

Far below the typical significance level of 0.05

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