Ways of knowing statistical concepts are reviewed. A general three-category structure for knowing is proposed: (a) calculations, (b) propositions, and (c) conceptual understanding. Test items were developed that correspond to the first category and to a partitioning of the two latter categories into words and symbols. Thirty-one items covering the five types were administered to 57 graduate students. Correlation of student scores on the 10-item calculations subtest and the 10-item propositions subtest was . 61, whereas the other two intercategory correlations were .40 (Calculations vs. Conceptual Understanding) and .37 (Propositions vs. Conceptual Understandings). The result suggest that students should be tested in more than one domain, and that instructors should expect students to develop conceptual understanding in addition to skills in computation.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education