Statistics education in psychology often falls disappointingly short of its goals. The increasing use of qualitative approaches in statistics education research has extended and enriched our understanding of statistical cognition processes, and thus facilitated improvements in statistical education and practices. Yet conceptual analysis, a fundamental part of the scientific method and arguably the primary qualitative method insofar as it is logically prior and equally applicable to all other empirical research methods--quantitative, qualitative, and mixed--has been largely overlooked. In this paper we present the case for this approach, and then report results from a conceptual analysis of statistics education in psychology. The results highlight a number of major problems that have received little attention in standard statistics education research. (Contains 1 figure.)