A Monte Carlo simulation study was conducted to examine the performance of α, λ2, λ4, μ2, ωT, GLBMRFA, and GLBAlgebraic coefficients. Population reliability, distribution shape, sample size, test length, and number of response categories were varied simultaneously. The results indicate that α and λ2 perform the worst overall. However, the performance of α is improved if the population reliability is high. λ4 is relatively unbiased but the most imprecise. μ2 and ωT perform relatively well under most conditions. GLBAlgebraic outperforms other coefficients under many conditions. GLBMRFA is useful under few conditions if the population reliability is high. The results corroborate previous suggestions that large samples, longer tests, higher number of response categories, and normally distributed results can make reliability estimates more dependable. Some insights on the interaction of these factors are provided. We discuss the findings compared to previous research. The complete R code used for the simulation is provided in the online supplement.
7 May 2024 in Advances in Methodology and Statistics
There are numerous reliability coefficients and α is the most popular. It is known that different coefficients can be appropriate in specific conditions and that α should not be used indiscriminately. However, some coefficients and conditions, particularly regarding the latent structure, lacked attention in previous research. In four Monte Carlo simulations, this study compared α, λ2, maximized λ4, λ4 based on locally optimal splits, μ2, Gilmer-Feldt, Kaiser-Caffrey α, Heise-Bohrnstedt Ω, Joreskog's ρ, ωtotal, algebraic greatest lower bound, greatest lower bound based on minimum rank factor analysis in every condition and also hierarchical ω and asymptotic ω hierarchical in multidimensional conditions. Findings suggest each of these coefficients can be useful at least in some conditions. Most differences in performance were observed in congeneric conditions and conditions with up to moderate loadings. Some coefficients were found to be more useful than previously considered. Results are discussed in the context of existing theory and previous Monte Carlo studies.
Combining two qualitative and a quantitative method, we explored whether school’s physical environment promotes multicultural values or reflects intergroup climate in two multiethnic communities in Croatia. Croatia offers unique context for this study because minority youth from two ethnic groups use their right on minority language education and hence attend separate minority schools. Results show that the representation of ethnic symbols in schools is a reflection of inter-ethnic relations in the specific intergroup context. Specifically, ethnic symbols are overrepresented in the post-conflict context compared to the more harmonious multi-ethnic community. In harmonious intergroup context, multiculturality is promoted by emphasizing common identity, and by giving space to symbols of both minority and majority group. However, in the conflicted intergroup setting we found overrepresentation of symbols emphasizing intergroup differences. Results of focus groups as well as of the quantitative survey confirm that schools physical environment reflects intergroup relations in each community.