Students' understanding of hypothesis testing in introductory tertiary-level statistics

The research study investigates students' understanding of hypothesis testing by exploring their conceptual and procedural knowledge of the topic.

Eighteen volunteer students from a large introductory service subject in statistics were interviewed three times during their semester of study - at the beginning of the semester, several weeks after their introduction to the topic of hypothesis testing, and after the final exam in the subject. This thesis reports mainly on the results from the third interview, in which students were required to complete a Concept Mapping task and two Hypothesis Testing tasks while talking aloud. On completion of each task, students were interviewed about their responses on these tasks. The focus is on four main concepts (hypothesis, significance level, p-value, significance) and the process of hypothesis testing. Students' protocols were analysed, and three case studies provided a deeper analysis of overall responses. Qualitative methods were used in the collection and analysis of data.

The study revealed that while some students had a good understanding of the hypothesis testing concepts and procedures, there were many deficiencies. In particular, students were often unable to define or explain a concept, give an example, or describe its relationships with other concepts. Less than half of the students could complete an Hypothesis Testing task by an approved method, and several solutions were incorrect at the decision step. There was evidence of some problems with statistical notation, and it was found that each procedural step in the hypothesis testing process had the potential to present difficulties. An overriding problem was associated with expressing ideas with statistical accuracy. The case studies showed that the relationship between conceptual and procedural knowledge was an interactive one. The relationship between conceptual and procedural knowledge was found to be so close that one type of knowledge depended on the other. Metacognition was needed to access the conceptual knowledge, which in turn improved the procedures.

This study provides empirical support for the move away from hand-worked hypothesis tests to an emphasis on the development of concepts. From the research, suggestions are offered for teaching with the latter emphasis, and improving students' overall understanding.