contingency table
Given a random sample of $N$ observations ${\text{\mathbf{Z}}}_{i}=({Y}_{i},{X}_{i1},\mathrm{\dots},{X}_{ik})$ where

1.
the response variables ${Y}_{i}$ are identically distributed as $Y$

2.
$Y$ is categorical in nature (coming from a multinomial distribution^{})

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 leftmost 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 

Canonical name  ContingencyTable 
Date of creation  20130322 14:32:53 
Last modified on  20130322 14:32:53 
Owner  CWoo (3771) 
Last modified by  CWoo (3771) 
Numerical id  11 
Author  CWoo (3771) 
Entry type  Definition 
Classification  msc 62H17 
\@unrecurse 