**4.1 Treatment of data**

Students' responses to the multi-tier questions provide four types of combinations of students' answers and reasons, namely: Correct Answer and Correct Reason (CACR) representing good scientific understanding; Correct Answer and Wrong Reason (CAWR) representing a false positive of students' unscientific understanding; Wrong Answer and Correct Reason (WACR) representing a false negative of students' unscientific understanding. These three categories are not discussed widely in this paper. Wrong Answer and Wrong Reason (WAWR) represents an actual student's unscientific understanding. This WAWR is the central aspect discussed in this regard and the prime category to be used in interpreting students' unscientific understanding.
