As a general rule, the repeated administration of tests measuring a given cognitive ability in the same participants reveals increased scores. This brings to life the well-known practice effect and it must be taken into account in research aimed at the proper assessment of changes after the completion of cognitive training programs. Here we focus in one specific research question: Are changes in test scores accounted for by the tapped underlying cognitive construct/factor? The evaluation of the factor of interest by several measures is required for that purpose. 477 university students completed twice a battery of four heterogeneous standardized intelligence tests within a time lapse of four weeks. Between the pre-test and the post-test sessions, some participants completed eighteen practice sessions based on memory span tasks, other participants completed eighteen practice sessions based on processing speed tasks, and a third group of participants did nothing between testing sessions. The three groups showed remarkable changes in test scores from the pre-test to the post-test intelligence session. However, results from multi-group longitudinal latent variable analyses revealed that the identified latent factor tapped by the specific intelligence measures fails to account for the observed changes.