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contingency table
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(Definition)
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documentclass[12pt]article pagestyleempty setlengthpaperwidth8.5in setlengthpaperheight11in par setlengthtopmargin0.00in setlengthheadsep0.00in setlengthheadheight0.00in setlengthevensidemargin0.00in setlengthoddsidemargin0.00in setlengthtextwidth6.5in setlengthtextheight9.00in setlengthvoffset0.00in setlengthhoffset0.00in setlengthmarginparwidth0.00in setlengthmarginparsep0.00in setlengthparindent0.00in setlengthparskip0.15in par usepackagehtml par usepackageamssymb,amscd usepackageamsmath usepackageamsfonts usepackagetabls usepackagemultirow par renewedcommandmultirowsetupcentering newlengthLL settowidthLL100 par begindocument par Given a random sample of htmladdnormallinkobservationshttp://planetmath.org/encyclopedia/Polychotomous.html
 where beginenumerate item the htmladdnormallinkresponse variableshttp://planetmath.org/encyclopedia/Polychotomous.html  are htmladdnormallinkidentically distributedhttp://planetmath.org/encyclopedia/IndependentIdenticallyDistributed.html as  item  is htmladdnormallinkcategoricalhttp://planetmath.org/encyclopedia/ContinuityAxiom.html in nature (coming from a htmladdnormallinkmultinomial distributionhttp://planetmath.org/encyclopedia/MultinomialDistribution.html) item each of the htmladdnormallinkexplanatory
variableshttp://planetmath.org/encyclopedia/Polychotomous.html  is categorical in nature endenumerate Then we can analyze the data by forming a emphcontingency table. The table is customarily formed by htmladdnormallinklabelinghttp://planetmath.org/encyclopedia/TotalLabeling.html the htmladdnormallinkcategorieshttp://planetmath.org/encyclopedia/Identity2.html for the response across the top, and then the htmladdnormallinkcombinationshttp://planetmath.org/encyclopedia/Choose.html of the levels for each explanatory variable down the left-most htmladdnormallinkcolumnshttp://planetmath.org/encyclopedia/ChuSpace.html. Then the htmladdnormallinkcellshttp://planetmath.org/encyclopedia/AttachingMap.html are filled with counts or frequencies of htmladdnormallinkoccurrenceshttp://planetmath.org/encyclopedia/Occurrence.html corresponding to the specific explanatory variable level
htmladdnormallinkcombinationhttp://planetmath.org/encyclopedia/CombinatoryLogic.html to the left and the response to the top. par The simplest example of a contingency table is where the response variable  comes from a htmladdnormallinkbinomial distributionhttp://planetmath.org/encyclopedia/BinomialProbabilityFunction.html (with two possible responses  and  ) and there is only one explanatory variable  , which has only two levels,  and  . This is an instance of a emph2 way contingency table: begincenter begintabular|c|c|c| hline &  & 
hline  &  & 
hline  &  & 
hline endtabular endcenter where  corresponds to the count or frequency of level  and response  . par textbfExample A penny  and a quarter  are each tossed separately 100 times. The htmladdnormallinkoutcomehttp://planetmath.org/encyclopedia/Game.html for each toss is recorded,  for head and  for tail. The htmladdnormallinknumbershttp://planetmath.org/encyclopedia/Number.html of heads and tails obtained from the tosses are recorded in the following 2 way table: begincenter begintabular|c|c|c| hline Coin Type &  & 
hline  & 45 & 55
hline  & 56 & 44
hline endtabular endcenter A emph3 way contingency table consists of one response variable and two explanatory variables. par textbfExample Four dice are used in an experiment to test whether they are more or less the “same” (having the same probability htmladdnormallinkdistributionhttp://planetmath.org/encyclopedia/GeneralizedFunction.html). Each die comes from a combination of one of two casinos,  and  , made by one of two manufacturers,  and  . Furthermore, no two dice have the same combination. Now, each dice is tossed 120 times and the outcomes (1 through 6)
are recorded. We have the following contingency table: begincenter begintabular|c|c|c|c|c|c|c|c| hline Casino & Manufacturer & 1 & 2 & 3 & 4 & 5 & 6
hline multirow2LL &  & 17 & 21 & 19 & 20 & 22 & 21
cline2-8 &  & 22 & 20 & 20 & 19 & 21 & 18
hline multirow2LL &  & 21 & 18 & 18 & 23 & 21 & 19
cline2-8 &  & 20 & 19 & 18 & 21 & 21 & 21
hline endtabular endcenter The explanatory variables are the casinos ( 's) and the manufacturers ( 's), and the response variable is the number appearing on the top htmladdnormallinkfacehttp://planetmath.org/encyclopedia/ImproperFace.html of a thrown die ( through  ). par enddocument
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"contingency table" is owned by CWoo. [ full author list (3) ]
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(view preamble)
Cross-references: face, distribution, numbers, outcome, binomial distribution, combination, occurrences, cells, columns, combinations, categories, labeling, explanatory variables, multinomial distribution, categorical, identically distributed, response variables, observations
There are 4 references to this entry.
This is version 8 of contingency table, born on 2004-08-10, modified 2007-12-18.
Object id is 6096, canonical name is ContingencyTable.
Accessed 5554 times total.
Classification:
| AMS MSC: | 62H17 (Statistics :: Multivariate analysis :: Contingency tables) |
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Pending Errata and Addenda
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