unconditional

Package‘Exact’

March28,2015

TypePackage

TitleUnconditionalExactTest

Version1.5

Date2015-03-27

AuthorPeterCalhoun

MaintainerPeterCalhoun<***********************>

DescriptionPerformsunconditionalexacttestsandpowercalculationsfor2x2contingency

itionalexacttestsareoftenmorepowerfulthanconditionalexacttestsandasymp-

totictests.

LicenGPL-2

NeedsCompilationno

RepositoryCRAN

Date/Publication2015-03-2807:37:34

Rtopicsdocumented:

Exact............................................1

..........................................3

.......................................6

Index9

ExactUnconditionalExactTestsfor2x2Tables

Description

ck-

nctiontocalculatethepowertodetectasignificant

differenceusingunconditionalexacttests.

Details

1

2Exact

Package:Exact

Type:Package

Version:1.5

Date:2015-03-27

Licen:GPL-2

Unconditionalexacttestscanbeperformedtotesttheindependenceofrowsandcolumnsina

itionaltests(suchasBarnard’sandBoschloo’xacttests)aremorepowerful

alternativesthanconditionaltests(suchasFisher’xacttest).P-valuescanbecomputedfor2x2

tablesunderthebinomialandmultinomialmodelsusingvariousteststatisticstofindthe’asor

moreextreme’tinomialmodelassumesonlythetotalsamplesizeisknownin

advance(commonincross-ctionalstudies),thebinomialmodelassumesonlytheroworcolumn

margins(butnotboth)arefixed(mostcommonsituation;occursinca-controlstudies),andthe

hypergeometricmodelassumesbothrowandcolumnmarginsarefixed(veryunlikelysituation;

onlydesignwhereFisher’stestshouldbeperformed).

andShuster

suggestedusingaZ-pooledstatistic,whichtheyfoundtobeuniformlymorepowerfulthanFisher’s

oorecommendedusingthep-valueforFisher’stestasthetest

thodbecameknownasBoschloo’stest,anditisalwaysuniformlymorepowerful

thanFisher’dAndressuggestedusingBarnard’onally,Berger

andBoospropodconsideringonlyvaluesofthenuisanceparameterthatareinaconstructed

confihereisstilla

disagreementonwhichteststatistictou,mostrearchersagreethatFisher’xacttestshould

hetestscanbecomputedinthispackage.

Note

lthanksgoestoPhilo

Calhoun,TalGalili,KamilErguler,RogerBerger,KarlHufthammer,andtheRcommunity.

Author(s)

PeterCalhoun

Maintainer:PeterCalhoun<***********************>

References

Barnard,G.A.(1945),156:177

Barnard,G.A.(1947)Signifirika,34:123-138

Berger,sD.(1994)Pvaluesmaximizedoveraconfidencetforthenuisanceparameter.

JournaloftheAmericanStatisticalAssociation89,1012-1016

Berger,R.(1994)Powercomparisonofexactunconditionaltestsforcomparingtwobinomialpro-

uteofStatisticsMimeoSeriesNo.2266

Berger,R.(1996)MorepowerfultestsfromconfianStatistician,50,

314-318

3

Boschloo,R.D.(1970),RaidConditionalLevelofSignificanceforthe2x2-tablewhenTesting

ticaNeerlandica,24,1-35

Cardillo,G.(2009)MyBarnard:averycompactroutineforBarnard’xactteston2x2matrix.

/matlabcentral/fileexchange/25760-mybarnard

Mato,res,M.(1997),SimplifyingthecalculationoftheP-valueforBarnard’stestand

ticsandComputing,7,137-143

Mehrotra,D.,Chan,I.,Berger,R.(2003),ACautionaryNoteonExactUnconditionalInferencefor

rics,59,441-450

Ruxton,haurM(2010),Goodpracticeintestingforanassociationincontingency

oralEcologyandSociobiology,64,1505-1513

Suissa,ster,J.J.(1985),ExactUnconditionalSampleSizesforthe2x2BinomialTrial,

JournaloftheRoyalStatisticalSociety,Ser.A,148,317-327

Trujillo-Ortiz,A.,Hernandez-Walls,R.,Castro-Perez,A.,Rodriguez-Cardozo,L,RamosDelgado,

N.A.,Garcia-Sanchez,R.(2004).Barnardextest:Barnard’Bfile.

[WWWdocument]/matlabcentral/fileexchange/6198-barnardextest

conditionalexacttestsfor2x2tables

Description

CalculatesBarnard’sorBoschloo’sunconditionalexacttestforbinomialormultinomialmodels

Usage

(data,alternative="",npNumbers=100,beta=0.001,

interval=FALSE,method="Z-pooled",model="Binomial",

=TRUE,=TRUE,=TRUE)

Arguments

dataAtwodimensionalcontingencytableinmatrixform

alternativeIndicatesthealternativehypothesis:mustbeeither"less","",or"greater"

npNumbersNumber:Thenumberofnuisanceparametersconsidered

betaNumber:Confidencelevelforconstructingtheintervalofnuisanceparameters

edifinterval=TRUE

intervalLogical:Indicatesifaconfidenceintervalonthenuisanceparametershouldbe

computed

methodIndicatesthemethodforfindingtablesasormoreextremethantheobrvedta-

ble:mustbeeither"Z-pooled","Z-unpooled","SantnerandSnell","Boschloo",

"CSM","CSMmodified",or"CSMapproximate".CSMtestscannotbecalcu-

latedformultinomialmodels

modelThemodelbeingud:mustbeeither"Binomial"or"Multinomial"

ical:Indicatesifrowmarginsarefiedif

model="Binomial"

gical:ceparametershouldbegenerated.

Onlyudifmodel="Binomial"

Logical:Indicatesifp-valueshouldberefinedbymaximizingthep-valuefunc-

edifmodel="Binomial"

Details

omialmodel

assumestheroworcolumnmargins(butnotboth)areknowninadvance,whilethemultinomial

ionaltestshavebothrowand

columnmarginsfi

thebinomialmodel,theurwillneedtoinputwhichmarginisfixed(defaultisrows).

LetXdenoteageneric2x2tablewithfixedsamplesizesn

1

andn

2

,X

0

denotetheobrvedtable,

andT(X)lhypothesiscanbewrittenasp

1

=p

2

≡p.

Thep-valuefunctionwithrowsfixedistheproductoftwoindependentbinomials:

P(X|p)=sup

0≤p≤1