contingency table

Given a random sample of N observations 𝐙i=(Yi,Xi1,,Xik) where

  1. 1.

    the response variables Yi are identically distributed as Y

  2. 2.

    Y is categorical in nature (coming from a multinomial distributionMathworldPlanetmath)

  3. 3.

    each of the explanatory variables Xij is categorical in nature

Then we can analyze the data by forming a contingency tableMathworldPlanetmath. The table is customarily formed by labeling the categories for the response across the top, and then the combinationsMathworldPlanetmathPlanetmath 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 r1 and r2) and there is only one explanatory variable X, which has only two levels, A1 and A2. This is an instance of a 2 way contingency table:

Title contingency table
Canonical name ContingencyTable
Date of creation 2013-03-22 14:32:53
Last modified on 2013-03-22 14:32:53
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 11
Author CWoo (3771)
Entry type Definition
Classification msc 62H17