Višefaktorska analiza varijance ponovljenih mjerenja

master's thesis

• Author: Nikolina Molnar
• Mentor: Anamarija Jazbec (mentor)
• Committee member: Anamarija Jazbec (predsjednik povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Glavna tema ovog rada je višefaktorska analiza varijance ponovljenih mjerenja. Analiza varijance ponovljenih mjerenja je statistička metoda kojom testiramo jednakost sredina na podacima čija mjerenja se ponavljaju. U prvom poglavlju, tj. uvodnome, djelomično je obrađen t-test za zavisne uzorke. Zatim je u drugom poglavlju obrađena analiza varijance s jednim i s vise 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 toga, obrađena je i analiza varijance ponovljenih mjerenja s jednim i sa više 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, kojima 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 primjerima su numerički obrađeni modeli i kroz njih smo pokazali konkretnu primjenu obrađenih metoda. Time smo diplomski rad učinili ne samo teoretskim nego i primijenjenim. 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, ona nije zastarjela. Štoviše, jedna je od najkorištenijih i najaktualnijih statističkih metoda koja se i dalje aktivno razvija.

Abstract (english)

The main topic of this paper was multifactorial analysis of variance of repeated measures. Analysis of variance of repeated measures is a statistical method used to test the equality of means having repeated measurements on same subjects. In first chapter partially was processed t-test for paired samples. In the second section we explained one-way and multi-way analysis of variance. 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. Afterwards, it was elaborated analysis of variance of repeated measures with one and multi factors. Already elaborated models were upgraded and it was easier to explain and understand further dividing of defined sum of squares. It was shown that a main cause of extra sum of squares were additional 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. Throughout examples models were numerically analyzed and through them we have shown concrete application processed methods. By that, this paper is not just theoretical but applied as well. Also, throughout examples was introduced program system SAS, which is one of the most popular tools for data analysis in academic and business world. Although the analysis of variance is used for a long time, for diverse statistical problems, it hasn’t become old fashioned. Moreover, it is one of the most used and up to date statistical method, which is still actively developing.

• Keywords: analiza varijance; podaci čija mjerenja se ponavljaju; ANOVA tablice; programski sustav SAS
• Keywords (english): analysis of variance; repeated measures; ANOVA tables; program system SAS
• Language: croatian
• URN:NBN: urn:nbn:hr:217:422351
• 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: 2019-01-25 12:47:26