Understanding the concept of P-value from the perspectives of two distinct definitions

Most lecturers still struggle to confidently explain the concept of p-value to their students in introductory research method courses. Often, they use the terms p-value and probability interchangeably in their explanations. This misconception, in many cases, is transferred to their students, and sometimes feature very prominently, even among seasoned instructors and researchers. This study provides a conceptual understanding of first-year postgraduate mathematics education students about the p-value from perspectives of two distinct definitions. The first defines p-value as the sum of three parts: The probability random chance would result in the observation, the probability of observing something else that is equally rare, and, the probability of observing something rarer or more extreme. The second defines p-value as the probability of obtaining results as extreme as the observed results of a statistical hypothesis, assuming that the null hypothesis is true. Forty-five (45) postgraduate mathematics education students from a mid-sized university in Ghana, were purposively selected for the study, after they had answered some diagnostic questions on the concept of the p-value.By working cooperatively in groups of three (3) using action research design, the students applied the two definitions in the tasks assigned to them by their instructor. The results indicated that the students’ conceptual understanding of p-value was enhanced when their instructor, through cooperative learning method, helped the students to apply the definitions in their concept acquisition. The implication to teaching and learning is that instructors should consciously introduce concepts that enable students to apply definitions, theorems, corollaries and lemmas. The use of a cooperative learning method enhanced the students’ learning outcome. The study concludes that a clear distinction between p-value and probability would be better understood and conceptualized if instructors teach their students concepts by applying definitions.

Index Terms— p-value, probability, conceptual understanding, concept, definitions.