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The performance of two polytomous item response theory models was compared to that of the dichotomous three-parameter logistic model in the context of equating tests composed of testlets. For the polytomous models, testlet scores were used to eliminate the effect of the dependence among within-testlet items. Traditional equating methods were used as criteria for both. The equating methods based on polytomous models were found to produce results that more closely agreed with the results of traditional methods.

How should we think about the concept of the testlet? How can testlets be better incorporated into test score analysis? Can there be a one‐item testlet?

The purpose of this study was to investigate the methods of estimating the reliability of school-level scores using generalizability theory and multilevel models. Two approaches, 'student within schools' and 'students within schools and subject areas,' were conceptualized and implemented in this study. Four methods resulting from the combination of these two approaches with generalizability theory and multilevel models were compared for both balanced and unbalanced data. The generalizability theory and multilevel models for the 'students within schools' approach produced the same variance components and reliability estimates for the balanced data, while failing to do so for the unbalanced data. The different results from the two models can be explained by the fact that they administer different procedures in estimating the variance components used, in turn, to estimate reliability. Among the estimation methods investigated in this study, the generalizability theory model with the 'students nested within schools crossed with subject areas' design produced the lowest reliability estimates. Fully nested designs such as (students:schools) or (subject areas:students:schools) would not have any significant impact on reliability estimates of school-level scores. Both methods provide very similar reliability estimates of school-level scores.