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