Višestruko testiranje hipoteza i Sorićeva metoda

master's thesis

• Author: Doris Zelić
• Mentor: Bojan Basrak (mentor)
• Committee member: Bojan Basrak (predsjednik povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu govorimo o problemu višestrukog testiranja hipoteza. Na početku rada dajemo uvod u problem testiranja statističkih hipoteza, navodimo osnovne pojmove te primjere testiranja. Zatim objašnjavamo kako, odnosno zašto dolazi do problema višestrukog testiranja hipoteza te neka predložena rješenja u statističkoj literaturi za taj problem. Upoznajemo se s osnovnim pojmovima koji se javljaju kada govorimo o višestrukom testiranju kao sto su pogreške tipa I i II, snaga testa, FWER (engl. familywise error rate) te navodimo neke od procedura za kontrolu grešaka. Velik dio ovog rada posvećujemo FDR-u (engl. false discovery rate) čiju je ideju dao dr. Branko Sorić. Definiramo FDR metodu, uspoređujemo ju sa FWER-om te govorimo o njenoj važnosti. Opisujemo i FDR proceduru koja je dizajnirana kako bi kontrolirala očekivani udio pogrešno odbačenih nul hipoteza, a u simulacijskoj studiji ilustriramo prednosti FDR metode koje su razlog njene velike popularnosti. Naglasimo da smo ovim radom samo zagrebali po površini ove vrlo važne tematike te da je literatura o višestrukom testiranju hipoteza vrlo bogata i da se u njoj konstantno javljaju novi doprinosi.

Abstract (english)

In this thesis we talk about the multiple testing problem. At the beginning of the thesis we introduce the problem of statistical hypotheses testing, its basic concepts and give some examples of testing. Then we explain how and why the problem occurs and present some solutions suggested in statistics literature. We introduce the basic concepts that arise in multiple testing, such as errors of type I and II, the power of the test, FWER (familywise error rate) and we list some of the procedures for error control. A big part of this thesis is dedicated to FDR (false discovery rate) whose idea goes back to dr. Branko Sorić. We define the FDR method, we compare it with FWER and we talk about its importance. We also describe the FDR procedure which is designed to control the expected proportion of incorrectly rejected null hypotheses. In a simulation study, we illustrate the benefits of the FDR method which are the reason for its great popularity. In this thesis we have only scratched the surface of this very important topic. The literature on multiple testing problem is very rich. New contributions and developments appear continuously.

• Keywords: višestruko testiranje hipoteza; procedura za kontrolu grešaka; FWER; FDR metoda
• Keywords (english): multiple testing problem; procedures for error control; FWER familywise error rate; FDR false discovery rate
• Language: croatian
• URN:NBN: urn:nbn:hr:217:095347
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-20 12:18:32