Analysis of Variance

Na početku rada detaljno se razmatraju osnovni pojmovi analize varijance (ANOVA), uključujući aritmetičku sredinu i njena svojstva te njihova veza s momentima oko sredine, posebno s varijancom kao drugim momentom oko sredine. Nadalje, obraća se pažnja na inferencijalnu statistiku te se objašnjavaju teorijske distribucije vjerojatnosti koje se primjenjuju u okviru analize varijance, s posebnim fokusom na karakteristike normalne distribucije, Studentove t-distribucije i Snedecorove f-distribucije. Rad dalje istražuje primjenu t-testa, proučavajući njegove pretpostavke i podjelu na jedan i dva uzorka. Prikazuju se primjeri primjene t-testa kako bi se olakšalo razumijevanje njegove svrhe i koristi. Također, istražuje se f-test, analizirajući njegove pretpostavke i pružajući primjere primjene. Ovaj dio istraživanja ima za cilj razjasniti ulogu f-testa u analizi varijance. U daljnjem tijeku rada, obrađuje se univarijatna analiza varijance, uključujući jednofaktorsku i dvofaktorsku analizu varijance, s naglaskom na identificiranje i procjenu varijacija između skupova podataka. U radu su prikazani primjeri provedbe ANOVA-e kako bi se ilustrirala njena praktična primjena u analizi statističkih podataka i donošenju zaključaka temeljenih na rezultatima istraživanja. Također, detaljno je objašnjena uloga analize varijance u ekonomiji i poslovnoj ekonomiji kroz primjere iz stvarnih istraživanja, kako bi se dobio uvid u primjenu ove metode u praksi.The beginning of the study thoroughly examines the fundamental concepts of Analysis of Variance (ANOVA), including the arithmetic mean and its properties, as well as their connection to moments around the mean, particularly the variance as the second moment around the mean. Furthermore, attention is given to inferential statistics and the explanation of theoretical probability distributions applied within the context of ANOVA, there is a special focus on the characteristics of the normal distribution, Student's t-distribution, and Snedecor's F-distribution. The research further explores the application of the t-test, studying its assumptions and the differentiation between one-sample and two-sample t-tests. Examples of t-test applications are provided to facilitate understanding of its purpose and benefits. Similarly, the research delves into the f-test, analyzing its assumptions and presenting practical examples of its application. This part of the research aims to clarify the role of the f-test in analysis of variance. In the subsequent sections, univariate analysis of variance is discussed, encompassing both one-way and two-way analysis of variance, with a focus on identifying and estimating variations among data sets. This study includes examples of conducting ANOVA to illustrate its practical application in the analysis of statistical data and drawing conclusions based on research results. Furthermore, the role of analysis of variance in economics and business economics is explained in detail through examples from real research to gain insight into the practical application of this method in practice