Testovi o očekivanju jedne ili više populacija - geometrijski pristup

master's thesis

• Title (english): Expectancy tests of one or more populations - geometric approach
• Author: Mirna Sabljak
• Mentor: Snježana Lubura Strunjak (mentor)
• Committee member: Snježana Lubura Strunjak (predsjednik povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-03-05, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kada provodimo znanstveno istraživanje, nije dovoljno samo pogledati dobivene rezultate i donijeti zaključak o problemu. Nužno je provesti statistički test i tek tada zaključiti što smo dobili tim istraživanjem. U testiranju postavljenih hipoteza koriste se različiti testovi i statistike, ovisno o problemu koji promatramo. U ovom diplomskom radu promatrali smo F-statistiku, a pitanje koje nas je zanimalo bilo je razlikuju li se promatrana očekivanja populacija. Glavna ideja rada bila je pomoću vektora objasniti zašto koristimo F-statistiku kod rješavanja takvih problema pa smo u prvom poglavlju ponovili osnovna znanja iz područja geometrije i statistike. Niz koraka u kojima smo to predočili nazvali smo geometrijski pristup. Potom smo promatrali jednu, dvije i tri populacije te kroz nekoliko primjera proveli sve korake geometrijskog pristupa te na taj način dobili F-statistiku i donijeli zaklju čke istraživanja. Tri glavna primjera preuzeta su iz [7], a dva su izmišljena i simulirana u programu R-u. Za bolje razumijevanje rad smo potkrijepili slikama koje su rađene u programima GeoGebra-i i R-u, a ideja za većinu njih preuzeta je iz glavne literature na kojoj se temelji rad [7].

Abstract (english)

When we conduct a scientific research it’s not enough to just look at the raw data to make conclusions. It is necessary to perform a statistical test and only then we can make a conclusion about the topic. Different tests and statistics are used in testing the hypothesis, depending on the problems we are interested in. In this thesis, we observed F-statistic and research subject was whether the observed population means differ. The main idea of the paper was to explain why we use F-statistics for such problems, while using vectors, so in the first chapter we reminded ourselves of the basic knowledges in the fields of geometry and statistics. We called the series of steps in which we presented this the geometric approach. We then observed one, two, and three populations and through several examples carried out all the steps of the geometric approach thus obtaining F-statistics and drawing research conclusions. Three main examples were taken over from [7] and two were made up and simulated in the R program. For a better understanding, the thesis substantiated with images made in Geogebra and R. The idea for most of them are also taken from the main literature [7] on which the paper is based.

• Keywords: znanstvena istraživanja; statistički test; F-statistika; program R; GeoGebra
• Keywords (english): scientific research; statistical test; F-statistic; R program; GeoGebra
• Language: croatian
• URN:NBN: urn:nbn:hr:217:062591
• Study programme: Title: Finance and Business Mathematics; 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: 2021-03-25 13:26:59