Analiza varijance ponovljenih mjerenja

master's thesis

• Author: Ivan Pažin
• Mentor: Anamarija Jazbec (mentor)
• Committee member: Anamarija Jazbec (predsjednik povjerenstva)
• Committee member: Luka Grubišić (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Aleksandra Čižmešija (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 ovome radu koji je podijeljen u tri poglavlja glavna tema nam je bila analiza varijance ponovljenih mjerenja. Analiza varijance ponovljenih mjerenja je statistička metoda kojom testiramo jednakost sredina na podacima čija mjerenja se ponavljaju. U prvom poglavlju, tako reći uvodnome, djelomično je obrađen t test. Točnije obrađen je t test za dva uzorka kao primjer testiranja jednakosti sredina. U drugom poglavlju proširili smo to testiranje na više uzoraka. Obrađena je univarijatna analiza varijance s jednim i s dva faktora. Objašnjena je varijabilnost rastavom na različite sume kvadrata, dan je matematički model, a sve statistike sa sumama kvadrata i pripadnim stupnjevima slobode su onda sažete u standardnim Anova tablicama. Nakon što je dobro pripremljen teren, obrađena je i analiza varijance ponovljenih mjerenja s jednim faktorom i sa dva faktora. Nadograđujući već obrađene modele bilo je lakše objasniti i razumjeti daljnje rastavljanje definiranih suma kvadrata. Kao glavni razlog dodatnih suma kvadrata pokazala su se dodatna mjerenja na istim subjektima, kojim homogeniziramo uzorak i smanjujemo neobjašnjenu varijabilnost. Rečeno je koje su prednosti, dan je model, navedene su i obrađene pretpostavke te su opet sve statistike dane u Anova tablicama. Na dva zanimljiva i stvarna primjera su numerički obrađena oba modela. Kroz primjere, kojih ima četiri: t test za 2 uzorka, dvofaktorski model analize varijance, jednofaktorski model analize varijance ponovljenih mjerenja i dvofaktorski model analize varijance ponovljenih mjerenja, pokazali smo konkretnu primjenu obrađenih metoda. Time smo diplomski rad učinili ne samo teoretskim nego i primjenjenim. Također smo se kroz primjere bolje upoznali sa programskim sustavom SAS, jednim od najpopularnijih alata za analizu podataka kako u akademskim krugovima tako i u poslovnom svijetu. Iako se analiza varijance već duže vrijeme primjenjuje za razne statističke probleme nije zastarjela. Štoviše, jedna je od najkorištenijih i najaktualnijih statističkih metoda koja se i dalje aktivno razvija.

Abstract (english)

In this thesis which is divided in three chapters the main theme was analysis of variance of repeated measures. Analysis of variance of repeated measures is a statistical method which tests the equality of means having repeated measurements on same subjects. In chapter one, which I would call introduction, partly was elaborated t test. To be correct it was elaborated t test for two samples as an example of testing the equality of means. In chapter two we expanded testing on more samples. It was elaborated univariate analysis of variance with one and two factors. The variability was explained by dividing on various sum of squares, it was given the mathematical model and all statistics with sum of squares and corresponding degrees of freedom are given in standard Anova tables. After good elaboration of analysis of variance was made, it was elaborated analysis of variance of repeated measures with one and two factors. Already elaborated models were upgraded and easier to explain and understand further dividing defined sum of squares. It was shown that a main cause of extra sum of squares were additional or more measurements on same subjects, which caused less unexplained variability as a result of more homogenized sample. The advantages were discussed, mathematical model was given, assumptions were named and elaborated and again all relevant statistics were given in standard Anova tables. On two interesting and real examples numerically were discussed both models. Throughout examples, which we had four: t test for two samples, two factor analysis of variance, one factor and two factor analysis of variance of repeated measures, concrete examples of elaborated models were shown. By that, this final thesis is not just theoretical but applied as well. Also, throughout examples program system SAS was introduced, which is one of the most popular tools for data analysis in academic and business world. Although analysis of variance is used for already longer period of time for diverse statistical problems it hasn’t become old fashioned. On contrary, it is one of the most used and up to date statistical method which is still actively developing.

• Keywords: analiza varijance ponovljenih mjerenja; t test; univarijatna analiza varijance; Anova tablice
• Keywords (english): analysis of variance of repeated measures; t test; univariate analysis of variance; Anova tables
• Language: croatian
• URN:NBN: urn:nbn:hr:217:530462
• 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 10:28:47