In confirmatory factor analysis quite similar models of measurement serve the detection of the difficulty factor and the factor due to the item-position effect. The item-position effect refers to the increasing dependency among the responses to successively presented items of a test whereas the difficulty factor is ascribed to the wide range of item difficulties. The similarity of the models of measurement hampers the dissociation of these factors. Since the item-position effect should theoretically be independent of the item difficulties, the statistical ex post manipulation of the difficulties should enable the discrimination of the two types of factors. This method was investigated in two studies. In the first study, Advanced Progressive Matrices (APM) data of 300 participants were investigated. As expected, the factor thought to be due to the item-position effect was observed. In the second study, using data simulated to show the major characteristics of the APM data, the wide range of items with various difficulties was set to zero to reduce the likelihood of detecting the difficulty factor. Despite this reduction, however, the factor now identified as item-position factor, was observed in virtually all simulated datasets.