I have 2 variables shape X and size Y. Shape $X$ has 4 states ($x_{0}, x_1, x_2, x_3$) and size $Y$ has 3 states ($y_0, y_1, y_2$).
The contingency table could look like this:
| Y \ X | $x_0$ | $x_1$ | $x_2$ | $x_3$ |
|---|---|---|---|---|
| $y_0$ | 350 | 50 | 40 | 0 |
| $y_1$ | 100 | 150 | 50 | 50 |
| $y_2$ | 10 | 90 | 10 | 5 |
How can I show that one combination ($x_0 / y_0$) is significantly likelier that the others? What is the correct "statistical" way to do that? Do I need the correlation coefficient for that?
Can I just say the probability that shape $x_0$ has size $y_0$ is $350/(350+50+40) = 0.795$ and that probability is higher than that for any other shape/size combination?