Suppose I have the following 2 way table and I perform a (Pearson) chi-squared test on it. With the null hypothesis: children's goals are independent of gender.
gender goal boy girl grades 117 130 popular 50 91 sports 60 30
X-squared = 21.4553, df = 2, p-value = 2.193e-05, so I accept the alternative hypothesis that children's goals is dependent on gender.
For further analysis, how would I find what this dependence might be? Could I look at the column percentages, as in the following table?:
gender goal boy girl grades 51.5 51.8 popular 22.0 36.3 sports 26.4 12.0 Total 99.9 100.1 Count 227.0 251.0
I could say that 51.5 and 51.8 are fairly close and 117 and 130 provide relativity good support to say that. Boys and girls both closely equally represented when having grades as their goal. And similarly I could say that more girls have goals to be popular than boys but more boys have goals to be more sporty than girls.
Would I still be able to make the same statement about boys and girls goals for grades if say there was only 13 boys and 17 girls that have their goal as grades out of 1000 boys and girls total? I would then have a very low support, what conclusion can I then make about that? More importantly how big of a support would I need to be able to make such a conclusion about their goals?
Are there also other things I can do after I the chi-squared test? (For example, if this was all the data I had, and no other variables to work with. I have got the individual responses as well in a data frame.)