Using Tree Diagrams as an Assessment Tool in Statistics Education

This study examines the potential of the tree diagram, a type of graphic organizer, as an assessment tool to measure students' knowledge structures in statistics education. Students' knowledge structures in statistics have not been sufficiently assessed in statistics, despite their importance. This article first presents the rationale and method for using tree diagrams as assessment tools in statistics education, followed by an empirical study examining the technical quality of tree diagram assessment. Thirty-seven university students enrolled in an introductory statistics course, and four statistics experts participated in the study. The results provide evidence of reliability and validity for the proposed function of using tree diagrams to measure knowledge structures in statistics education. As reliability evidence, the interrater reliability of tree diagram scoring is high (Pearson's r = .96); alpha coefficient of the 21 linked vertex pairs in tree diagrams is .89. As validity evidence, experts performed better than novices on the tree diagram assessment; students' performance with the tree diagram is significantly correlated with their performance on statistics achievement tests (Pearson's correlation coefficient r = .62); tree diagrams are sensitive to the discrepancies in students' knowledge structures, and most students considered tree diagrams helpful to their organization of statistics knowledge.