For contingency tables I don't understand why the Null Hypothesis is 'independent'.
We calculate Sum(Observed^2 / Expected) - N and compare this with the chi-squared distribution table.
Sum(Observed^2 / Expected) - N = 4
Chi-square value = 5.1
So 4 < 5.1 and we do NOT reject the Null Hypothesis, they are independent.
But if 4 < 5.1, then the difference between all Observed and Expected is smaller than our Critical Value, so surely they are correlated and therefore not independent?
I got confused because I was doing this question:
and in the answer:
they state the Null Hypothesis is "no difference", which read like they are not independent?