The main aim of this study was to introduce the ConQuest program, which is used in the analysis of multivariate and multidimensional data structures, and to show its applications on example data structures. To achieve this goal, a basic research approach was applied. Thus, how to use the ConQuest program and how to prepare the data set for analysis were explained step by step. Then, two example applications were made considering the multidimensional structures. Finally, different sources of variability (e.g., item, student, rater, gender), which are both multidimensional and independent of each other, were performed by considering different sources of variability together. According to the analyses, the dimensionality of the data structures must be examined in the analysis process. If the data structure is multidimensional, appropriate multidimensional IRT analyses should be performed.