There has been widespread concern expressed by members of the statistics education community in the past few years about the lack of any real understanding demonstrated by many students completing courses in introductory statistics. This deficiency in understanding has been particularly noted in the area of inferential statistics, where students, particularly those studying statistics as a service course, have been inclined to view statistical inference as a set of unrelated recipes. As such, these students have developed skills that have little practical application and are easily forgotten. This thesis is concerned with the development of understanding in statistical inference for beginning students of statistics at the post-secondary level. This involves consideration of the nature of understanding in introductory statistical inference, and how understanding can be measured in the context of statistical inference. In particular, the study has examined the role of the sampling distribution in the students' schemas for statistical inference, and its relationship to both conceptual and procedural understanding. The results of the study have shown that, as anticipated, students will construct highly individual schemas for statistical inference but that the degree of integration of the concept of sampling distribution within this schema is indicative of the level of development of conceptual understanding in that student. The results of the study have practical implications for the teaching of courses in introductory statistics, in terms of content, delivery and assessment.