Comparison of observed and estimated cell counts

The hypothesis of independence is assessed by asking whether the observed and estimated cell counts are 'sufficiently close' — are the observed counts consistent with the counts estimated under independence?

Recruitment source and success

Hypotheses

Did a sample contingency table come from a population in which the categorical row and column variables, X and Y are independent? This question can be formalised with the hypotheses,

H0 :  X and Y are independent
HA :  X and Y are dependent  

Distribution of sum of squares