I'm trying to test for dependence between gender and passing a study unit. The contingency table is as below

enter image description here

gengrade <-matrix(c(23930, 31742, 3499, 5315), nrow =2, ncol = 2, byrow = T)
chisq.test(gengrade, correct = FALSE)

Pearson's Chi-squared test

data: gengrade
X-squared = 33.609, df = 1, p-value = 6.739e-09

The mosaic plot is something like this:

enter image description here

Can anyone help me understand if I should keep the hypothesis that there is no dependency between gender and passing a unit, or have I done something wrong


1 Answer 1


This is an example of something that is statistically significant but (probably) of no practical importance.

The p value is very small: "p-value = 6.739e-09" or .0000000067 (if I've hit 0 the right number of times, scientific notation is good). That is, if there were no relation between these variables in the whole population, then you would be very unlikely to get a chi-square at least as high as this in a sample the size of the one you have.

But the mosaic plot shows that the relationship is very weak. In most cases, it's so weak that no one will be interested. Certainly it seems of no practical importance here, in terms of the relationship between sex and passing.

The relevant proportions are .1276 and 0.1434.

You didn't tell us which variable is which (you'll want to add that info if you write this up) but it might be "12.76% of girls and 14.34% of boys fail". Do you care that 1.5% more of one sex pass?


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