Derive the relationships among the eight versions of odds ratios of Section 2.2.2.

When twovariables(orrowandcolumn)areactuallyassociated,wemaywanttoknowthe
nature oftheassociation.Therearemanyindicesthathavebeendevelopedtocharacterize
the associationbetweentwovariables.Ifoneofthetwovariablesisanoutcomeandthe
other agroupindicatorasinacase-controlorrandomizedtrialstudywithtwotreatment
conditions, onemayusethedierencebetweentheproportionsasameasureofassociation
betweenthetwovariables.Othercommonmeasuresforassessingassociationbetweenthe
outcome andgroupindicatorincludetheoddsratioandrelativerisk.Ifbothvariables
are outcomesmeasuringsomecharacteristicsofinterestforsubjectsinasinglesample,
correlations areusedasmeasuresofassociation.Westartwiththetwo-samplecasewith
one variablebeingthegroupindicator.