The chi-square test of independence is used to analyze the frequency table (i.e. contengency table) formed by two categorical variables. The chi-square test evaluates whether there is a significant association between the categories of the two variables
Chi-square test examines whether rows and columns of a contingency table are statistically significantly associated.
Null hypothesis (H0): the row and the column variables of the contingency table are independent. Alternative hypothesis (H1): row and column variables are dependent
Determine whether passing rate is independent from gender
# create a matrix of past/fail tally by gender (malefemal)
dt <- matrix(c(45,5,15,15), nrow=2, byrow=T)
rownames(dt) <- c("female", "male") # add row names
colnames(dt) <- c("pass", "fail") # add column names
dt # display matrix values pass fail
female 45 5
male 15 15chisq <- chisq.test(dt) # run chi-square test
chisq$p.value # check p.value if significant[1] 0.0001889622Determine whether the roles of husbands and wives are independent of household chores
# source: http://www.sthda.com/english/wiki/chi-square-test-of-independence-in-r
chores <- data.table::fread("C:/jun/FirstSem24-25/Stat 2024/Labs/Chi/Chores.csv")
chores Chore Wife Alternating Husband Jointly
<char> <int> <int> <int> <int>
1: Laundry 156 14 2 4
2: Main_meal 124 20 5 4
3: Dinner 77 11 7 13
4: Breakfeast 82 36 15 7
5: Tidying 53 11 1 57
6: Dishes 32 24 4 53
7: Shopping 33 23 9 55
8: Official 12 46 23 15
9: Driving 10 51 75 3
10: Finances 13 13 21 66
11: Insurance 8 1 53 77
12: Repairs 0 3 160 2
13: Holidays 0 1 6 153chisq <- chisq.test(chores[,2:5])
chisq
Pearson's Chi-squared test
data: chores[, 2:5]
X-squared = 1944.5, df = 36, p-value < 2.2e-16contrib <- 100*chisq$residuals^2/chisq$statistic
round(contrib, 2) Wife Alternating Husband Jointly
[1,] 7.74 0.27 1.78 2.25
[2,] 4.98 0.01 1.24 1.90
[3,] 2.20 0.07 0.60 0.56
[4,] 1.22 0.61 0.41 1.44
[5,] 0.15 0.13 1.27 0.66
[6,] 0.06 0.18 0.89 0.63
[7,] 0.09 0.09 0.58 0.59
[8,] 0.69 3.77 0.01 0.31
[9,] 1.54 2.40 3.37 1.79
[10,] 0.89 0.04 0.03 1.70
[11,] 1.71 0.94 0.87 1.68
[12,] 2.92 0.95 21.92 2.28
[13,] 2.83 1.10 1.23 12.45corrplot::corrplot(contrib, is.cor = FALSE)