# contingency table

Given a random sample of $N$ observations $\textbf{Z}_{i}=(Y_{i},X_{i1},\ldots,X_{ik})$ where

1. 1.

the response variables $Y_{i}$ are identically distributed as $Y$

2. 2.

$Y$ is categorical in nature (coming from a multinomial distribution)

3. 3.

each of the explanatory variables $X_{ij}$ is categorical in nature

Then we can analyze the data by forming a contingency table. The table is customarily formed by labeling the categories for the response across the top, and then the combinations of the levels for each explanatory variable down the left-most columns. Then the cells are filled with counts or frequencies of occurrences corresponding to the specific explanatory variable level combination to the left and the response to the top.

The simplest example of a contingency table is where the response variable $Y$ comes from a binomial distribution (with two possible responses $r_{1}$ and $r_{2}$) and there is only one explanatory variable $X$, which has only two levels, $A_{1}$ and $A_{2}$. This is an instance of a 2 way contingency table:

Title contingency table ContingencyTable 2013-03-22 14:32:53 2013-03-22 14:32:53 CWoo (3771) CWoo (3771) 11 CWoo (3771) Definition msc 62H17