This study examined the possibility of a curvilinear relationship between statistics anxiety and performance in a statistics course. Eighty-three undergraduate students enrolled in an introductory course completed measures of statistics anxiety and need for achievement at seven points during the semester in conjunction with six tests. Statistics anxiety scores were reliable internally and across time. Statistics anxiety decreased during the term yet paradoxically became more strongly related to performance. Curvilinear models were better predictors of test performance than linear, suggesting a mid-range optimal level of statistics anxiety. However, students' need for achievement proved not to mediate the relationship between anxiety and performance. The authors suggest ways these findings may influence future research in statistics anxiety and classroom management of anxiety. (Contains 3 figures and 2 tables.)