19 May Elementary Statistics JMP Assignment 01
Performing ContingencyAnalysis
UsingtheFitYbyXorContingencyPlatform
(1) Click on the Help tab in JMP and select Sample Data.
(2) Click on the following option: See an Alphabetical List of all Sample Data Files
(3) Click on the Car Poll.jmp sample data table
Make an attempt to answer the following questions and if you find that you will take more than 60 seconds then look at the section below on Contingency Table.
(1) What is the number of cars that are both large and come from America?
(2) What is the percentage of all cars that are both large and come from America?
(3) What is the percentage of large cars that come from America?
(4) What is the percentage of American cars that are large?
ContingencyTable
TheContingencyTableisatwo-wayfrequencytable.Thereisarowforeachfactorlevelandacolumnforeach responselevel.
ToproducetheplotshowninFigure6.1,follow the instructions in the example below:
TheContingencyorFitYbyXplatformletsyouexplorethedistributionofacategorical(nominalor ordinal)variableYacrossthelevelsofasecondcategoricalvariableX.TheContingencyplatformisthe categoricalbycategoricalpersonalityoftheFitYbyXplatform.Theanalysisresultsincludeamosaicplot, frequencycounts,andproportions.
Figure 6.1 A ContingencyTable
ExampleofContingencyAnalysis
ThisexampleusestheCar Poll.jmpsampledatatable,whichcontainsdatacollectedfromcarpolls.The dataincludesaspectsabouttheindividualpolled,suchastheirsex,maritalstatus, andage.The data also includesaspectsaboutthecarthattheyown,suchasthecountryoforigin,thesize,andthetype.Examine therelationshipbetweencarsizes(small,medium,andlarge)andthecars’countryoforigin.
1. Using the open Car Poll.jmp sample datatable.
2. Select Analyze > Fit Y byX.
3. Select size and click Y,Response.
4. Select country and click X,Factor.
5. ClickOK.
Thefollowingtable explainstheconclusionsthatyoucanmakeaboutthesecarsusingtheContingencyTable.
Number Description Label inTable
36 NumberofcarsthatarebothlargeandcomefromAmerica Count
11.88% Percentage of all cars that are both large and come from America (36/303)a.
85.71% Percentage of large cars that come from America (36/42)b
31.30% Percentage of American cars that are large (36/115)c.
Total%
Col%
Row%
MosaicPlot
Themosaicplotisagraphicalrepresentationofthetwo-wayfrequencytableorContingencyTable.Amosaicplotisdividedintorectangles,sothattheareaofeachrectangleisproportionaltotheproportionsof theYvariableineachleveloftheXvariable
Notethefollowingaboutthemosaicplotin the Figure above:
• Theproportionsonthex-axisrepresentthenumberofobservationsforeachleveloftheXvariable,which is country.
• Theproportionsonthey-axisatrightrepresenttheoverallproportionsofSmall,Medium,andLargecars for the combined levels (American, European, andJapanese).
•
Fromthemosaicplotandlegendin the Figureabove,noticethefollowing:
• Very few Japanese cars fall into the Large sizecategory.
• The majority of the European cars fall into the Small and Medium sizecategories.
• The majority of the American cars fall into the Large and Medium sizecategories.
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