Development of an Item Bank of Order and Graph by Applying Multidimensional Item Response Theory

Article excerpt


This study aimed to develop an item bank of Order and Graph of Mattayomsuksa 1 level (grade 7). The samples were 4,800 lower secondary students from 34 schools in northeastern area of Thailand, academic year 2011 chosen through multi-stage random sampling. The research tool used in the study was a multiple choicetest of an Order and Graph lesson by applying multidimensional item response theory. Parameter were analyzed by confirmatory factor analysis by applying multidimensional normalogive model with guessing of the program normalogive harmonic analysis robust method (NOHARM). Discrimination power and Easiness intercept were equated through non-orthogonal procrustes method. The study results indicated that there were 59 items out of 140 passed the test standard.

Key words: Item bank; Cognitive process; Multidimensional item response theory (MIRT)

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The three methods for managing an effective learning achievement are having clear educational goals and objectives, having effective learning procedures for students to get cognitive, affective and psychomotor domains, and having an appropriate effective evaluation (Kanjanawasri, 2009, p. 2-6).

The well-known learning process that was widely used was the cognitive domain of Bloom et al. (1956) who divided 6 learning processes of the brain including, knowledge, understanding, applying, analyzing, synthesizing and evaluation. In 2001, Anderson et al. (2001, p. 27-31) had developed this learning process, changing the keywords and rearranging the processes with two dimensions; cognitive process and knowledge. The cognitive dimension included of 6 processes: remembering, understanding, applying, analyzing, evaluation and creating respectively. The knowledge dimension consisted of 4 parts: factual knowledge, conceptual knowledge, procedural knowledge and meta knowledge.

The educational evaluators believe that the inspecting model of the cognitive dimension is based on item response process. Therefore, psychological theory is considered as the base of inspecting the cognitive dimension (Rupp & Templin, 2008a, p.225). According to this, the cognitive dimension inspecting model is undoubtedly associated with psychology and measurement theories which consist of 3 types including classical test theory (CTT), unidimensional item response theory (IRT) and multidimensional item response theory (MIRT). Multidimensional Item Response Theory Models (MIRTM) are the most effective model and consists of latent variables. Each of them indicates its latent trait for the inspection (Haberman, 2008, p. 204-205; Rupp & Templim, 2008b, p.78-80; Sinhary et al, 2007, p. 22).

The model is from factor analysis of Structural Equation Modeling (SEM) and it is the implement of IRT (Reckase, 2009, p. 63). MIRTM can effectively explain a tester's answers from the test since it can analyze lots of one's factors at the same time, (Embretson & Reise, 2000, p. 82).

In conclusion, the development of the item bank by applying MIRT will decrease the number of the test items since it can explain many factors of learners at the same time while the effectiveness is better than CTT and IRT (Frey & Seitz, 2009, p. 89).


This study aimed to develop Mattayomsuksa one's item bank of Order and Graph by applying multidimensional item response theory with its specific objectives as follows;

1. To create the test on Order and Graph of Mattayomsuksa 1 level.

2. To find the quality of the test that its parameter value was analyzed through multidimensional normal ogive model with guessing.

3. To arrange an item bank of Order and Graph, Mattayomsuksa 1 level.



The samples of this study were 4,800 lower secondary students from 34 schools in northeastern area of Thailand. 3,046 students were from large schools, 1,415 of them were from medium schools and the rests were from small schools. …


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