Table Of Content

EXACTUNCONDITIONALINFERENCEFOR2x3AND2x2x2 CONTINGENCYTABLES By GERALDG.CRANS ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1999 ©Copyright1999 by GeraldG.Crans Tomyfather ACKNOWLEDGEMENTS IwouldliketoexpressmygratitudetoProfessorJonathanShusterforhisguidance and patience throughout this dissertation. The workingenvironment was perfect for me, and his suggestions and modifications were invaluable to this work. His contributiontothisdissertationwascrucial. IwouldalsoliketothankProfessorRandolphCarterforgivingmetheopportunity toworkwithhisgroupasastatistician. Thejobhasbeenquiteinteresting,andthe amountofpracticalstatisticalknowledgethatIhaveobtained, fromworkingwith him,hasbeensubstantial. MyappreciationextendstoProfessorsMalay GhoshandAndrew Rosalskyfor readingthisdissertationandprovidinghelpfulsuggestions. Finally, Iwould liketothankmyfatherforhisconfidenceandencouragement throughoutmylife. iv TABLEOFCONTENTS ACKNOWLEDGEMENTS iv ABSTRACT vii CHAPTERS 1 LITERATUREREVIEW 1 1.1 Introduction 1 1.2 AHistoryoftheMaximizationMethod 4 1.3 MotivationforanAlternativetoConditionalMethods 13 1.4 StatisticalPowerComparisons 14 2 MAXIMIZINGTHENULLPOWERFUNCTION 20 2.1 Introduction 20 2.2 FindingtheMaximumof}{B) 21 2.3 FindingtheMaximumofg(9) 26 3 THE2x3CONTINGENCYTABLE 30 3.1 Introduction — 30 3.2 TheConditionalApproachtothe2x3ContingencyTable — 32 3.3 DeterminingSampleSizesUsingtheConditionalApproach — 35 3.4 TheAsymptoticApproachtothe2x3ContingencyTable 42 3.5 AnExactUnconditionalTestforthe2x3ContingencyTable . 43 3.6 Results 47 4 THE2x2x2CONTINGENCYTABLE 51 4.1 Introduction 51 4.2 TheConditionalApproachtothe2x2x2ContingencyTable 53 4.3 DeterminingSampleSizeRequirementsUsingtheConditional Approach 56 4.4 TheAsymptoticApproachtothe2x2x2ContingencyTable 63 4.5 AnExactUnconditionalTestforthe2x2x2ContingencyTable 65 4.6 Results 67 v APPENDICES A THESETf/3 69 B CHAPTER3TABLES 70 C CHAPTER3GRAPHS 78 D CHAPTER4TABLES 85 E CHAPTER4GRAPHS 94 F FORTRANPROGRAMS 105 REFERENCES 146 BIOGRAPHICALSKETCH 148 vi AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillment oftheRequirementsfortheDegreeof DoctorofPhilosophy EXACTUNCONDITIONALINFERENCEFOR2x3AND2x2x2 CONTINGENCYTABLES By GeraldG.Crans May1999 Chairman: JonathanJ.Shuster Majordepartment: Statistics Exactunconditionalhypothesistestingmethodsinthecontextofthe2x2bino- mialtrial,2x2multinomialtrial,andthecomparisonofcorrelatedproportionsex- hibitasuperiorpoweradvantagewhencomparedwithexactconditionalapproaches. However,untilnowtherehavebeennoattemptsmadetocompareunconditionaland conditionalmethodsinamoreelaboratesetting, i.e. testingscenariosthatinvolve morethanjustasinglenuisanceparameter. Thiswasduetotheunavailabilityof techniquespresentforcomputingthemaximumofnullpowerfunctionsinvolvingsev- eralnuisanceparameters. Amethodologyisdevelopedhereinwhichprovidesameanstocomputethemax- imumofnullpowerfunctionsthatareoftwopossibleforms. Thesetwoformscor- respondtomultinomialandbinomiallikelihoods,whichcancontainseveralnuisance parameters. Asspecialcases,the2x3contingencytabletocomparetwoindependent trinomialdistributions,andthe2x2x2contingencytabletocompareindependent proportionsattwodifferentstrataareconsidered. vii Fortheequalsamplesizecase,exactcriticalvaluesofthePearsonchi-squaretest forcomparingtwoindependenttrinomialdistributionsarecomputedandtabulated forn= 10(1)70, a = 0.025and a= 0.05. Tofacilitatecomparisons, atechnique fordeterminingsamplesizerequirementswhenusingtheconditionalapproachwas developed. For a = 0.025and apowerof0.80, samplesize requirements forthe conditionaltestwereoftentimessmallerthanthosefortheexactunconditionalchi squareand, infrequently, thesamplesizerequirementswerelarger. Graphsofthe nullpowerfunctionsandthecomparisonofthecriticalregionssuggestthatthecon- ditionalp-valueisabetterteststatisticthanPearson's. Forthe2x2x2tableexactcriticalvaluesoftheMantelHaenszelteststatistic withcontinuitycorrectionarecomputedandtabulatedforn=10(1)50,a=0.025 anda=0.05,wherethesamplesizenisthesameforeachbinomialtrial. Again, amethodwasdevelopedtodeterminesamplesizerequirementsfortheconditional approach,socomparisonscouldbemade. Fora—0.025andapowerof0.80,sample sizerequirementsforeachmethodwereestablished. Theresultsprovedinconclusive, asneithermethodoutperformedtheother. However,graphsofthenullpowerfunc- tionsindicated that theconditional p-valueismuch morestablethanthe Mantel Haenszelstatistic,andcomparisonsoftherespectivecriticalregionsindicatethatthe conditionalp-valueisthebetterstatistic. viii CHAPTER 1 LITERATUREREVIEW 1.1 Introduction Inhypothesistestingprocedureswhereboththenullandalternativehypotheses aresimple,theoptimalsolutionforagivenlevelaiscompletelyspecifiedbytheNey- manPearsonlemma. However,whenthedistributionoftheteststatistic,underH0, dependsonadditionalparameterswearenotinterestedin,formallycallednuisance parameters,thenthesolutionisanythingbutclear. Suppose,forexample,thatwe areinterestedinconductingahypothesistestabouttheparameter9,butthedistri- butionofthestatisticusedforthetestingprocedurealsodependsonthenuisance parameter7. Theproblemwearefacedwithishowtoconductourhypothesistest inthepresenceofthisunknownnuisanceparameter. Therearenumeroussolutionstothenuisanceparameterproblem,andBasu(1977) summarizesthese. Ofthemethodshereviews,onlythreewillbeconsideredinwhat follows. Italsoshouldbenotedthatofthesethree,onlytwoareregularlyusedin practice. Thefirst,andperhapsmostcommonmethod,isusingasymptotictheory. Here, allparametersexceptthosebeingtestedarereplacedbyestimates. Inmost casestheestimatesarethemaximumlikelihoodestimates,whichundercertainreg- ularityconditionsareconsistent. Sincetheyareconsistent,wecanuselimittheory resultssuchasSlutsky'stheorem(inconjunctionwiththecentrallimittheorem)to derivetheasymptoticnulldistributionoftheteststatistic. Itfrequentlyturnsout thattheresultingdistributionissimpleandwelltabulated. Asanexample,thePear- sonchi-squareteststatisticforcomparingtwoindependentbinomialproportionshas 1 2 anasymptoticchi-squarenulldistributionwithonedegreeoffreedom. Theadvantage ofusingasymptoticmethodsissimplicity. However,asthisisanasymptoticresult, itmaynotworkwellforsmallsamples. Thesecondmethodistheconditionalapproach. Sinceweoftenworkwithlikeli- hoodsthataremembersofexponentialfamilies,wecanusethemethodsofLehmann (1982)toeliminatenuisanceparameters. Forexample,supposeweareinterestedin testingahypothesisconcerningtheparameter9inthepresenceofanunknownnui- sanceparameter7. Also,supposethatXandYarerandomvariablesthatarejointly sufficientfor(#,7),andthejointprobabilitydistributionof(X,Y)isamemberofan exponentialfamily,i.e. fxY{x,y;0,i)=C{6,-y)exp(tx(8)x+t2(y)y+g(x,y)). Since7isunknown,wecanrestrictourclassofteststoa-similartests. Usingthe conditionaldistributionofXgivenY,wecandevelopauniformlymostpowerfulun- biased(UMPU)testforthehypothesisabout9. Themajorcriticismofthismethod isthatifXandYarediscrete, theconditionaldistributionofX given Ywill be discreteaswell, sothatarandomizationprocedureisneededtoobtainatestsize ofexactlya. However,sincerandomizedtestsarenotusedinpractice,theresult- ingnon-randomizedconditionaltestwillbeconservative. Anotherdisadvantageof theconditionalmethodisthatwearerestrictedtoaconditionalsamplespace. All statisticalinferenceprocedureswillbedonewithrespecttothisconditionalspace. Thiswillposeaproblemtothenon-statisticians, inthattheinterpretationofthe attainedsignificancelevel (p-value) isnolongerappealing, orforthatmattereas- ilyunderstandable. Whenconditional methodsareusedintheapplied literature, suchasmedicineoragriculture,theconditionalnatureofthep-valueisalmostnever mentionedinthepublication. The third technique is the maximization method. Here, the size ofa test is determinedbymaximizingthenullpowerfunctionoverthedomainofthenuisance

Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables PDF

158 Pages·1999·5.4 MB·English

by Crans, Gerald G

#americana #univ_florida_smathers #UFRDS

Checking for file health...

Download

Upgrade Premium

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Download Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables PDF Free - Full Version

by Crans, Gerald G| 1999| 158 pages| 5.4| English

Download Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables by Crans, Gerald G in PDF format completely FREE. No registration required, no payment needed. Get instant access to this valuable resource on PDFdrive.to!

Free Download PDF

About Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables

No description available for this book.

Detailed Information

Author:	Crans, Gerald G
Publication Year:	1999
Pages:	158
Language:	English
File Size:	5.4
Format:	PDF
Price:	FREE

Download Free PDF

Safe & Secure Download - No registration required

Why Choose PDFdrive for Your Free Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables Download?

100% Free: No hidden fees or subscriptions required for one book every day.
No Registration: Immediate access is available without creating accounts for one book every day.
Safe and Secure: Clean downloads without malware or viruses
Multiple Formats: PDF, MOBI, Mpub,... optimized for all devices
Educational Resource: Supporting knowledge sharing and learning

Frequently Asked Questions

Is it really free to download Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables PDF?

Yes, on https://PDFdrive.to you can download Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables by Crans, Gerald G completely free. We don't require any payment, subscription, or registration to access this PDF file. For 3 books every day.

How can I read Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables on my mobile device?

After downloading Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables PDF, you can open it with any PDF reader app on your phone or tablet. We recommend using Adobe Acrobat Reader, Apple Books, or Google Play Books for the best reading experience.

Is this the full version of Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables?

Yes, this is the complete PDF version of Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables by Crans, Gerald G. You will be able to read the entire content as in the printed version without missing any pages.

Is it legal to download Exact unconditional inference for 2 x 3 and 2 x 2 x 2 contingency tables PDF for free?

https://PDFdrive.to provides links to free educational resources available online. We do not store any files on our servers. Please be aware of copyright laws in your country before downloading.

The materials shared are intended for research, educational, and personal use in accordance with fair use principles.