Bringing successful teaching approaches for stimulating conceptual change to normal classrooms has been a major challenge not only for teachers but also for researchers. In this study, we focused on the relationship between cognitive conflict and responses to anomalous data when students are confronted with a counterintuitive demonstration in the form of a discrepant event. The participants in this study were 96 secondary school students (9th grade) from S. Korea. We investigated students' preconceptions of motion by administering a written test. After the exam, we presented a demonstration that may have conflicted with the ideas held by students. We then investigated the relationship between students' cognitive conflict and responses to anomalous data by using a Cognitive Conflict Level Test (CCLT). Results showed that cognitive conflict initiated the first step in the process of conceptual change. Anxiety was an especially crucial component of cognitive conflict, affecting the relationship between cognitive conflict and students' responses. In addition, superficial conceptual change was found to be the most common response.