Current testing approaches for specifying a BIB design differ in that instead of assigning items to examinees, items are assigned to clusters, which are assigned to booklets, which are in turn assigned to examinees. Specifically, the total item pool is divided into t clusters of items (adding an advantage that the number of items per cluster can vary). The t clusters are then assigned to b booklets. Each booklet is of equal length with k clusters. Every cluster t appears only once in any booklet and r times across all booklets, with each pairofclustersappearingλtimes.Parametersthenspecifyingthedesignaret,b,r,k,andλ.Thisimpliesthatrt=bk.Oneimportantconstraintonthisdesignist≤b.Thatis,thenumberofclustersshouldnotexceedthenumberof booklets. In practical applications, discussed subsequently, some of these conditionsarenotmet.Namely,λislessthan1inatleastoneinternationallarge-scale assessment, rendering this design not strictly a BIB design but a partially balanced incomplete block (PBIB) design (Giesbrecht and Gumpertz 2004).Adisadvantageoftheconditionλ<1isthatnoteveryclusterappearsin a booklet with every other cluster, making the possibility of a pair-wise, cluster-specific context effect difficult to evaluate and control. In addition, item linking is heterogeneous as item pairs are consequently unbalanced.
proceso
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- El banco total de ítems se divide en varios clústeres.
- Cada cuadernillo contiene el mismo número de clústeres.
- Cada clúster aparece varias veces en distintos cuadernillos.
- Idealmente, cada par de clústeres aparece el mismo número de veces.
Sin embargo, en la práctica esto no siempre se cumple. En algunas evaluaciones internacionales:
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