In this study, probabilities of preservice middle school mathematics teachers’ possession of four fundamentalcognitive skills required for learning and teaching statistics and probability topics were examined by using thelog-linear cognitive diagnostic model, which is one of the cognitive diagnostic models. Moreover, theprobabilities of preservice teachers’ possession of these skills were investigated according to gender, universityranking, and grade level variables. Hence, it was examined whether there was a significant relationship betweenthe probabilities of having each skill and these variables. A Statistical Reasoning Test, which was developed byArican and Kuzu in 2019, measured preservice teachers’ possession of four critical skills was used in collectingthe data. These four skills included representing and interpreting data, drawing inferences about populationsbased on samples, selecting and using appropriate statistical methods to analyze data, and understanding andapplying basic concepts of probability. In the 2016-2017 academic year, the test was applied to 456 preserviceteachers selected from four different universities in Turkey, and probabilities of their possession of each attributewere calculated. Later, the relationship between the preservice teachers’ test scores and gender was examinedby using the Mann-Whitney U test, and the relationship between their test scores and ranking of the attendeduniversity and grade level were examined using the Kruskal Wallis-H test. Although probabilities of thepreservice teachers’ possession of these four skills did not significantly differ according to gender, somesignificant differences were detected for university ranking and grade level variables