Statistični pristopi pri analizi trdnosti

COTIČ, JASNA (author), Blagus, Rok (mentor)

Obravnavamo statistično analizo podatkov o trdnosti cirkonijeve oksidne keramike, ki spada med krhke biomateriale. Za trdnost je značilna Weibullova porazdelitev in ob uporabi linearnih modelov ostanki niso normalno porazdeljeni. Alternativi sta transformacija z rangi in permutacijski testi. Velikost in moč teh metod preverjamo na simuliranih podatkih iz normalne in Weibullove porazdelitve. Pomembnejše razlike med metodami se pokažejo le pri zelo asimetrični Weibullovi porazdelitvi, ki je v pravih podatkih ne srečamo. Linearni modeli postanejo konzervativni in zmanjša se jim moč. Ob ohranjeni velikosti se zmanjša tudi moč permutacijskih testov, moč transformacije z rangi pa se celo poveča. Dodatno preverjamo velikost in moč testov pri različnih obravnavah opisnih spremenljivk. Pri nepravilni obravnavi imajo testi napačno velikost in precenjeno moč. Rezultate simulacij ilustriramo na pravih podatkih in zaključimo, da so linearni modeli dovolj zanesljiva metoda za statistično analizo.

• Language: Slovenian
• Keywords: trdnost krhkih materialov, Weibullova porazdelitev, linearni modeli, permutacijski testi, transformacija z rangi
• Work type: Master's thesis/paper
• Organization: FE - Faculty of Electrical Engineering
• Year: 2016
• PID: 20.500.12556/RUL-80146
• Publication date in RUL: 21.01.2016

Secondary language

• Language: English
• Title: Statistical analysis of strength data

Abstract

This thesis addresses the statistical analysis of zirconia bioceramic strength data. Strength of brittle materials is known to follow the Weibull distribution. When linear models are used, the assumption of normality is not met. Rank transformation and permutation tests can be used instead. We perform a simulation study concerning the type I error and power on normal and Weibull distributed data. We show that notable differences only emerge in extremely asymmetric Weibull distributions not relevant for real data. For linear models, we detect a reduction in the type I error and power. With the type I error preserved, the power loss of permutation tests and the power increase of rank transformation is evident. Additionally, we consider different treatments of categorical variables and show that inappropriate treatment results in an inflated type I error and overestimated power. We also present a real data set and conclude that linear models are a reliable method to analyze the strength data.

• Keywords: trdnost krhkih materialov, Weibullova porazdelitev, linearni modeli, permutacijski testi, transformacija z rangi