# Contingency Table Interpretation

Tags:
1. Nov 4, 2014

### Mogarrr

1. The problem statement, all variables and given/known data
10.24 Is there any relationship between the type of treatment and the response? What form does the relationship take?

Here's that data (column variables are responses):
$\newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{|c|c|c|c|c|} \hline Treatment & +Smear & +Smear,-Culture & -Smear,-Culture & Total\T \\\hline Peniclillin \T & 40 & 30 & 130 & 200 \\\hline Spectinomycin(low dose)\T & 10 & 20 & 70 & 100 \\\hline Spectinomycin(high dose)\T & 15 & 40 & 45 & 100 \\\hline Total\T & 65 & 90 & 245 & 400 \\\hline \end{array}$

2. Relevant equations

3. The attempt at a solution
I've already done a chi-square test and found what was hinted in the question, the treatment and response are not independent.

What's a good way to describe the relationship?

I've thought of combining 2 treatment so that I could do Cochran Armitage Trend Test, but given the treatments, I see no clear way of combining categories.

I'm also thinking of commenting on the conditional probabilities and how they differ from the marginal probabilities. (I think the probabilities in the cells can be thought of as conditional probabilities). For example: the probability of a negative smear, negative culture given the treatment was a high dose of spectinomycin is $\frac {45}{100}$ compared to the probability of a negative smear, negative culture, which is $\frac {245}{400}$.

2. Nov 10, 2014