Višestruko uspoređivanje

master's thesis

• Author: Almeida Hasić
• Mentor: Anamarija Jazbec (mentor)
• Committee member: Anamarija Jazbec (predsjednik povjerenstva)
• Committee member: Aleksandra Čižmešija (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Luka Grubišić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U primjeni nailazimo na problem odlučivanja postoje li razlike između više populacija te između kojih od njih se prepoznaju značajnije razlike. Ukoliko se pokazalo da za tri ili više uzoraka ANOVA odbacuje nultu hipotezu, to jest da postoji značajna razlika među uzorcima tada koristimo post-hoc testove nakon analize varijance čije su pretpostavke o homogenosti varijance uzoraka, te normalnosti podataka zadovoljene. Takvu vrstu testiranja nazivamo parametrijsko testiranje i tu spada višestruko uspoređivanje pomoću Fisherove LSD procedure koja glasi kao najslabija, Tukey i Newman-Keuls testova, Dunnettovog testa za usporedbu s kontrolnim uzorkom te Bonferroni testa. Za posebnu vrstu višestrukog uspoređivanja, kontraste, najpogodniji je Shefféov test. Druga vrsta testiranja provedena u radu, je neparametrijski analogon ANOVA proceduri i njenim post-hoc testovima. U svim testovima višestrukog uspoređivanja, jednake veličine uzoraka su poželjne za maksimalnu snagu i robusnost. U ovom radu prikazana je teorijska pozadina višestrukog uspoređivanja te su navedena tri primjera na kojim je jasno prikazana razlika među različitim testovima. Prikazano je kako se podaci mogu obrađivati sa i bez računalne podrške. Kako bi rezultati i zaključci bili što točniji korišten je programski paket SAS te su navedeni svi potrebni kodovi.

Abstract (english)

In the practice, there is a problem of deciding if there are differences between several populations and between which of them we can recognize significant differences. If it turns out that ANOVA rejects the null hypothesis for three or more treatments, in other words that there exists a significant difference between treatments, than we use post-hoc tests after the analysis of variance whose assumptions of homogeneity of variance of the treatments and population normality of data are met. This type of testing is called parametric tests, and it includes multiple comparisons using Fisher's LSD procedure which is known as the weakest, Tukey and Newman-Keuls tests, Dunnett's test for comparison with the control, and the Bonferroni test. For a special type of the multiple comparisons, contrasts, the best suited is the Sheffe’s test. Another type of tests used in this thesis is the nonparametric analogue to the ANOVA procedure and its post-hoc tests. In all multiple comparison tests, equal sample sizes are desirable for maximum power and robustness. This thesis shows the theoretical background of multiple comparisons and it contains three examples in which is clearly shown the difference between various types of tests. It shows how the data can be processed with and without computer support. Statistical analysis software – SAS was used to achieve the most accurate results and conclusions. All required codes are listed above.

• Keywords: ANOVA; analiza varijance; parametrijsko testiranje; višestruko uspoređivanje; Fisherova LSD procedura; Tukey testovi; Newman-Keuls testovi; Dunnettov test; Bonferroni test; Shefféov test; SAS
• Keywords (english): ANOVA; analysis of variance; parametric tests; multiple comparisons; Fisher's LSD procedure; Tukey tests; Newman-Keuls tests; Dunnett's test; Bonferroni test; Sheffe’s test; SAS
• Language: croatian
• URN:NBN: urn:nbn:hr:217:970538
• 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: 2019-01-29 12:45:06