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Properties of two-phase testing procedures
Krausová, Eliška ; Omelka, Marek (referee) ; Kulich, Michal (advisor)
In the present work we study properties of two-phase testing procedures which formally verify assumptions by performing some test ( first phase) and subsequently calculate a test statistic selected according to the results of the previous test (second phase). In the beginning we describe two-phase testing procedures and mention some literature, in which they are recommended. We try to derive formula for the combined level and power of the whole two-phase testing procedure. After that we illustrate their properties through simulation studies.
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Statistical applications of urn models
Navrátil, Radim ; Omelka, Marek (referee) ; Pawlas, Zbyněk (advisor)
This work shows various applications of urn models in practice. First, basic properties of the occupancy distribution are derived together with its asymptotic approximation. This model is applied and generalized in the theory of database systems for records search from a given database. An application to random texts is mentioned, namely the computation of the expected number of missing and common words in random texts. There are presented exact formulas, their asymptotic approximations and the approximations via occupancy distribution. Then, some urn models, which are used in the randomized response theory for finding out respondents' answers to sensitive questions, are described. These models are compared according to their accuracy and respondents' goodwill to answer. Finally, two non-parametric tests of empty boxes are derived, one for the hypothesis whether a random sample comes from a given population and the second for the hypothesis whether two independent random samples come from the same population. The powers of these tests are compared with commonly used tests for these hypotheses.
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Effect of indicators on adjusted score in English language test MANA 2005
Protivínský, Tomáš ; Zvára, Karel (referee) ; Omelka, Marek (advisor)
N5zev prace: VHv indikatoru na dosa^ene skore v testu z anglickeho jazyka MANA2005 Autor: Tomas" Protivinsky Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalarske prace: Ing. Marek Omelka E-mail vedouciho: omelka@karlin.mff.cuni.cz Abstrakt: Prace analyzuje data ziskana testy Maturita naneffsto 2005. Zabyva se vlivem jednotlivych faktoru na dosazene skore z anglickeho jazyka, hodnoti je z hlcdiska jejich vyznamnosti a snazi se odhalit vztahy mezi nimi. Nejdfive uvazuji jednoduche modely s jednim vysve-tlujicim faktorem. Zde jsem se zamčfil pf edevgim na typ Skoly (gymnazium, SOS, SOU) a jeji polohu (die pfislugnosti ke kraji) a pohlavi zaka. V praci take kratce diskutuji mozn6 pficlny pozorovanych rozdilu. Tyto dilcl vysledky pak na zdv^r porovnavam s celkovou analyzou, ktera do modelu zahr- nuje vSechny sledovane faktory. Zahrnul jsem i strucny popis zamgfeni a organizace testu Maturitananecisto. Klicova slova: Linearni regrese, analyza rozptylu Title: Effect of indicators on adjusted score in Englishlanguage test MANA 2005 Author: TomaS Protivinsky Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Marek Omelka Supervisor's e-mail address: omelka@karlin.inff.cuni.cz Abstract:The thesis analyzes a data acquired in the test Maturita naneclsto 2005. It...
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