| Inferential statistics is important for scientific research. This study investigated the nature of the knowledge that supports the ability to choose appropriate statistical techniques for applied research situations. Knowledge used by statistical experts (statistical consultants and mathematical statisticians) and novices (graduate students in mathematics education and research methods) was compared in two kinds of statistical tasks that varied in goal specificity. Subjects compared research scenarios from the perspective of choosing a statistical technique (specified goal), and directly compared statistical techniques (open goal). Individuals were interviewed using repertory grid technique. Contrasts were performed between and within expert and novice groups on the extensiveness, connectedness and the task-adaptedness of the knowledge they used to perform the tasks. The knowledge used by novices was analyzed qualitatively in relation to the coursework reported by their instructors.;Results showed that, of the four types of knowledge used for statistical modeling of applied research situations, research design knowledge comprised more than 50% of the knowledge experts used. Theoretical and procedural elements of the knowledge constituted relatively smaller portions. When comparing statistical techniques, the knowledge used by the two kinds of experts evidenced significant differences. Statistical consultants used more research design knowledge and mathematical statisticians used more theoretical knowledge, indicating better adaptations to applied and theoretical tasks respectively. This finding gives evidence for multiple expertise in inferential statistics. Although there were no significant differences in the extensiveness of the knowledge used by experts and novices for statistical technique tasks, experts' knowledge-use was found to be much more interconnected and better adapted to the goal of applied problem solving. Knowledge used by novices for statistical techniques was found to be limited to prototypical versions, and possessing faulty conceptions. Instructors' emphasis on certain themes of knowledge did not necessarily match how novices used these themes.;There were two implications for helping students to develop selection skills in inferential statistics: (1) statistical techniques should be taught in relation to the features of research design with which they can be used, and (2) conceptual connections between the statistical techniques should be explicitly taught. |
