Using Rasch scaled stage scores to validate orders of hierarchical complexity of balance beam task sequences

These studies examine the relationship between the analytic basis underlying the hierarchies produced by the Model of Hierarchical Complexity and the probabilistic Rasch scales that places both participants and problems along a single hierarchically ordered dimension. A Rasch analysis was performed on data from the balance-beam task series. This yielded scaled stage of performance for each of the items. The items formed a series of clusters along this same dimension, according to their order of hierarchical complexity. We sought to ascertain whether there was a significant relationship between the order of hierarchical complexity (a task property variable) of the tasks and the corresponding Rasch scaled difficulty of those same items (a performance variable). It was found that The Model of Hierarchical Complexity was highly accurate in predicting the Rasch Stage scores of the performed tasks, therefore providing an analytic and developmental basis for the Rasch scaled stages.