Generalizability theory (G theory) allows researchers to assess the many sources of variance inherent in complex standard setting procedures involving the determination of cut scores. The flexibility of G and D studies provides a way to conceptualize and quantify the results of different standard settings once the universe of admissible observations and the universe of generalization are defined. The current article applies a multivariate single-facet design for estimating standard errors of cut scores. For practical purposes, several multivariate D study designs are used to investigate what effect various panel sizes and test lengths have on the precision of the standard setting process. The current study demonstrates the advantages and usefulness of multivariate G theory in determining the accuracy of cut scores in practical applications of standard setting procedures.
Selecting an appropriate cognitive diagnostic model (CDM) for data analysis is always challenging. Studies have explored several model fit indices for CDMs. The common results of these studies indicate that Qmatrix misspecifications lead to poor performance of the model fit indices in the context of CDMs. Thus, this study explored whether model fit indices improve performance with a modified Q-matrix. The average class size has reduced to 23 students in Taiwan because of the low birth rate; therefore, the study sought the effect of sample size on the performance of model fit indices. The results showed that Akaike's information criterion (AIC) was an excellent model fit index in small samples. Model fit indices with the modified Q-matrix presented superior performance.
Taiwan has, from 2006, participated in five Programme for International Student Assessment (PISA) surveys. This chapter discusses Taiwan’s performance in PISA and its implications. At first, the education system and the process of educational reform in Taiwan were described. Then Taiwan’s performances for reading, math, and science in PISA were delineated. Taiwanese students have had consistently excellent performance for math and science; its reading performance, although not as outstanding as those for math and science, has improved significantly from 2009 to 2018. The gender gap in reading, in favour of female students, has narrowed, and the gender gap in math and science has been small. Educational equity, especially between rural and urban students, has also improved from 2006 to 2018. The proportion of high performers in reading and the proportion of low performers in reading, math, and science has increased from 2006 to 2018, while the proportions of top performers in math and science have decreased. These findings are interpreted from the perspectives of cultural beliefs, changes in the education system and national assessment, government investment in the related domains, and the nature of the PISA assessment.
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