Analiza varijance ponovljenih mjerenja

Pažin, Ivan (2014) Analiza varijance ponovljenih mjerenja. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

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.

Item Type: Thesis (Diploma thesis)
Supervisor: Jazbec, Anamarija
Date: 2014
Number of Pages: 45
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 16 Jun 2015 09:47
Last Modified: 16 Jun 2015 09:47
URI: http://digre.pmf.unizg.hr/id/eprint/4051

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