Title Utvrđivanje indikatora uspješnosti studiranja Author Mislav Zorko Mentor Miljenko Marušić (mentor)Committee member Miljenko Marušić (predsjednik povjerenstva)Committee member Zvonimir Bujanović (član povjerenstva)Committee member Pavle Goldstein (član povjerenstva)Committee member Nikola Sarapa (član povjerenstva)Granter University of Zagreb Defense date and country 2015-09-25, Croatia Scientific / art field, NATURAL SCIENCES Abstract U ovom diplomskom radu promatramo uzorak studenata koji su upisali studij matematike u razdoblju od 2005. do 2011. godine. Uzorak razdvajamo u dva djela, prvi prije uvođenja državne mature i drugi za vrijeme. U prvom uzorku postoji promjena u računarskim kolegijima, dok drugi uzorak ima jednake kolegije kroz godine. Definirali smo pojam uspješnog studenta kao studenta koji je položio sve kolegije prve godine u roku. Rad se sastoji od pet poglavlja. U prvom poglavlju dajemo deskriptivnu statistiku promatranog uzorka. Zaključili smo da ne postoji statistički značajna razlika između generacija koje su slušale različite računarske kolegije (na nivou značajnosti \(\alpha = 0.05\)), te pretpostavili da su u tom uzorku kolegiji jednaki kroz godine. Nadalje, analizirali smo prvo bodove iz srednje škole (oznaka \(\mathcal{BS}\)), a zatim i bodove s prijemnog ispita/državne mature (oznaka \(\mathcal{BT}\) ). Uz stupčaste dijagrame, box-plotove i tablice s osnovnim statističkim veličinama, proveli smo test analize varijance (ANOVA). U slučaju kada je postojala statistički značajna razlika (za nivo značajnosti \(\alpha = 0.05\)) između barem dvije grupe, proveli smo dodatno Tukey test i rezultate dali pregledno u tablici. Na kraju prvog poglavlja provodimo analizu uspješnih studenata. Promatramo udio uspješnih studenata kroz godine, te položenosti pojedinih kolegija. Uz grafičke prikaze i osnovne tablice, provodimo testove o proporcijama. Svi rezultati dani su pregledno u tablicama. Drugo i treće poglavlje daju teorijski aspekt logističke regresije. Dan je uvod u univarijatnu i multivarijatnu analizu, definirani su glavni pojmovi i uvedene opće oznake. Također je dana pozadina prilagodbe modela logističke regresije i testiranja značajnosti koeficijenata. Dana su tri glavna testa: test omjera vjerodostojnosti, Waldov test i Score test. Na kraju poglavlja dana je pozadina procjene intervala pouzdanosti. Četvrto poglavlje daje primjenu osnovnih univarijatnih i multivarijatnih modela logističke regresije na promatranom uzorku studenata. Promatrali smo utjecaj nezavisnih varijabli \(\mathcal{BS}\) i \(\mathcal{BT}\) na zavisnu dihotomnu varijablu uspjeha (\(\mathcal{US}\)). Zaključili smo da postoji veza između uspjeha studenta i promatranih nezavisnih varijabli. Pomoću ROC krivulja zaključili smo da je nezavisna varijabla \(\mathcal{BT}\) bolja u procjeni uspjeha od nezavisne varijable \(\mathcal{BS}\), ali da je optimalno promatrati multivarijatni model koji sadrži obje varijable. Uz standardne testove i tablice, dani su grafički prikazi logističkih funkcija zajedno s \(95\%\) prugama pouzdanosti i pripadne ROC krivulje. Proveli smo pripadni Waldov test za značajnost koeficijenata i zaključili da su u svim univarijatnim i multivarijatnim modelima promatrane nezavisne varijable značajne. Također smo promatrali i dio uzorka studenata koji su položili sve kolegije prvog semestra studija. U svim modelima varijable su bile značajne (nivo značajnosti \(\alpha = 0.05\)). U zadnjem poglavlju dajemo općeniti algoritam za procjenu parametara multivarijatnog modela. Također je dana i implementacija koda u programskom jeziku Matlab.
Abstract (english) In this thesis we look at a sample of students who enrolled in the study of mathematics in the period from 2005 to 2011. The sample is split into two parts, the first before the introduction of the state graduation and the other after. In the first sample there is a change in computer courses, while the second sample has the same courses over the years. We have defined the concept of a successful student as a student who has passed all courses in the first year of the term. Thesis consists of five chapters. In the first chapter we provide descriptive statistics of the sample. We concluded that there was no statistically significant difference (significance level is \(\alpha = 0.05\)) between the generation that listened to various computer courses and we assumed that in the sample courses are the same through the years. Furthermore, we analyzed the first variable, points from high school (\(\mathcal{BS}\)), and then points to the entrance examination/State graduation (\(\mathcal{BT}\)). With bar charts, box-plots and tables with basic properties, we conducted a test of analysis of variance (ANOVA). In the case where there was a statistically significant difference (significance level is \(\alpha = 0.05\)) between at least two groups, we conducted further Tukey test and the results are given in the tables. At the end of the first chapter we conduct an analysis of successful students. We looked at the share of successful students over the years and at individual courses. With graphics and basic tables, we conducted tests of proportions. All results are presented in tables. The second and third chapter gives the theoretical aspect of the logistic regression. An introduction to univariate and multivariate analysis is given and main concepts are defined. There is also a background of adapting logistic regression model and testing the significance of the coefficients with three tests: likelihood ratio test, Wald test and Score test. At the end of the chapter we give background of estimation of confidence intervals. The fourth chapter provides the application of basic univariate and multivariate logistic regression model to the observed sample of students. We looked at the impact of the independent variables \(\mathcal{BS}\) and \(\mathcal{BT}\) on the dependent dichotomous variable success (\(\mathcal{US}\)). We concluded that there is a link between student success and the observed independent variables. Using the ROC curve, we have concluded that the independent variable \(\mathcal{BT}\) is better in assessing the success of the independent variables \(\mathcal{BS}\), but that it is optimally to use multivariate model that includes both variables. In addition to the standard tests and tables, we give graphical representations of logistics functions with \(95\%\) stripes reliability and associated ROC curve. We conducted the corresponding Wald test for the significance of the coefficients and concluded that in all univariate and multivariate models observed independent variables are significant. We also looked at part of the sample of students who have passed all courses in the first semester. All model variables were significant (significance level \(\alpha = 0.05\)). In the last chapter we give a general algorithm for estimating parameters of multivariate models. There is also an implementation of the code in the programming language Matlab.
Keywords
uzorak studenata koji su upisali studij matematike u razdoblju od 2005. do 2011. godine
uzorak studenata prije uvođenja državne mature
uzorak studenata nakon uvođenja državne mature
uspješni student
test analize varijance (ANOVA)
Tukey test
logistička regresija
univarijatna analiza
multivarijatna analiza
test omjera vjerodostojnosti
Waldov test
Score test
ROC krivulja
Keywords (english)
sample of students who enrolled in the study of mathematics in the period from 2005 to 2011
sample of students before the introduction of the state graduation
sample of students after the introduction of the state graduation
successful student
Tukey test
analysis of variance (ANOVA)
logistic regression
univariate analysis
multivariate analysis
tests of proportions
Wald test
Score test
ROC curve
Language croatian URN:NBN urn:nbn:hr:217:933930 Study programme Title: Mathematical Statistics Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2019-02-20 13:18:44
