delo diplomskega seminarja
Teja Rupnik (Author), Maja Pohar Perme (Mentor)

Abstract

V svoji diplomski nalogi sem prikazala izpeljave velikosti vzorca pri različnih statističnih raziskavah in različnih pogojih, ki so jim rezultati raziskav morali zadostovati. Prikazala sem, kako formulo za določitev velikost vzorca izpeljemo iz intervala zaupanja oziroma stopnje značilnosti, iz moči testa, kdaj uporabimo aproksimacije in postopek iteracij ter kako ustrezno velikost vzorca poiščemo s tabeliranjem in iskanjem ničel. Izpeljave sem prikazala na asimptotsko normalno porazdeljenih, eksaktno normalno porazdeljenih, nesimetrično porazdeljenih in $\chi^2$-porazdeljenih testnih statistikah za oceno deleža, povprečne vrednosti, Pearsonovega koeficienta korelacije, razmerja obetov in variance. Ugotovila sem, da iz normalno porazdeljenih testnih statistikah, formulo za velikost vzorca izpeljemo direktno iz intervala zaupanja in moči testa, medtem ko pri testnih statistikah, ki niso normalno porazdeljene, uporabimo aproksimacije in iteracijo ali poiščemo iskano velikost vzorca s pomočjo tabeliranja ter z iskanjem ničel.

Keywords

matematika;statistična raziskava;velikost vzorca;moč testa;intervali zaupanja;Cohenova velikost učinka;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL MF - Faculty of Medicine
Publisher: [T. Rupnik]
UDC: 519.2
COBISS: 18442073 Link will open in a new window
Views: 878
Downloads: 284
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Other data

Secondary language: English
Secondary title: Sample size determination
Secondary abstract: In my thesis I was solving sample size estimations problems in different statistical analysis with different conditions, witch had to be fulfilled. I demonstrated how to dissolve equation for sample size from confidence interval or significance level alpha, from power of test, when to use approximation and iteration, how to estimate sample size from generated table and with root finding. I will show derived formulas from asymptotic normal distribution, exact normal distribution, skewed distribution and $\chi^2$-distribution for sample proportion, sample average, Pearson correlation coefficient, odds ration and sample variance. I've discovered that for normal distributed test statistics sample size formula is dissolved directly from confidence interval and power of test, while for non-normal distributed test statistics we use approximations and iteration or we determined sample size based on generated table and with root finding.
Secondary keywords: mathematics;statistical analysis;sample size;power of test;confidence interval;Cohen effect size;
Type (COBISS): Final seminar paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages: 34 str.
ID: 10961113
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