Chi-square Tests

 Teaching Tips 2: The connection between Chi-squared and z

For each student in class, I recorded eye color and whether the student wore glasses or corrective lens.
     Lens     No lens
Light eyes     8     12
Dark eye     43     47

If we use a Chi-squared test, with df =1, we find Chi-squared= 1.21 with p-value = .5716.

Expected values     Lens     No lens
Light eyes     10.2     9.8
Dark eye     40.8     39.2

If we use a two proportion z-test we find z = -1.10 and p-value = .5716.

Students also observe that when the (-1.10)^2 = 1.21