# Post hoc Chi square non significant

I am interested to see if there is any relationship between eye color and whether someone is a vegan or not. The data is as follows:

      Vegan Non vegan
Blue     29        23
Green    15        32
Brown     3         9


I ran a Chi-squared test of association and the result is significant.

    Pearson's Chi-squared test

data:  vegan
X-squared = 7.4115, df = 2, p-value = 0.02458


However, when I ran the post-hoc of this, it turns out the p-values are not significant.

Adjusted p-values used the bonferroni method.

1  Blue vs. Green 0.0255 0.0766
2  Blue vs. Brown 0.1069 0.3206
3 Green vs. Brown 0.7388 1.0000


What does this mean? If I look at the counts and expected counts of each group, I can see that people who are vegan tend to have blue eyes, and non-vegan tend to have green eyes.

R code you can try:

library(fifer)
vegan <-
matrix(c(29,15,3,23,32,9),
nrow = 3,
dimnames =
list(c("Blue", "Green", "Brown"),
c("Vegan", "Non vegan")))
chisq.test(vegan)
chisq.post.hoc(vegan, control = "bonferroni")