# Conceptualizing the “Core” in Applied Statistics

I enjoyed reading the sagely ideas offered by Bonnie and Marty that describe the core or central concepts to be taught in an applied statistics course. For me, it is essential early in the semester to have my statistics students (I teach in business, psychology and sociology programs) demonstrate their understanding of the critical connections between a theoretical distribution, sampling distribution and a sample distribution in the context of hypothesis testing and parameter estimation. Such an interrelated conceptualization opens students’ eyes not only to the language inherent in these two forms of inferential analysis, but also sets the stage for subsequent (and repetitive) use of this framework across various statistical procedures as I apply them to “the real world.”

Related to this discussion, for me, is another core component often unspoken in the halls of our academies and seldom part of an applied statistics course: the theory-research connection. None of us in academe operate in a purely applied world sans theory or theoretical applications, or inductive versus deductive thought. Why else would we run paired sample t tests on those cute and fuzzy rats in a t-maze unless we had some inductive or deductive logic underlying our trial efforts? More to the point: Even areas of curricular assessment, so essential to matters of strategic planning and programmatic and institutional accreditation, fuse the worlds of theory and statistical research. Do we want to measure critical thinking in the classroom, across your program and/or, in the aggregate, at your university? Then we should understand the connections between and among the following: paradigms, theory, concepts, propositions, abstract continuum, operationalization, variables, and hypotheses. (Note: For an interesting graphical approach to this pedagogy, I’d like to offer a PowerPoint presentation I use that’s tied to an earlier publication I had on the subject. It usually takes no more than a class period to cover this lecture – and it even includes a closed-ended model – see Figure 5 – to assess student learning. Here is the link: http://worldofevergreen.com/Theory-Research.pdf.  Though this document is formatted as a .pdf file for my students, you are welcome to the PowerPoint presentation on request.)

If one of our classroom objectives, beyond those typically found in an applied statistics course, is relevance, then such an approach will help students better understand (1) why they are taking a statistics class when nearly all of their other classes are geared toward theory, (2) how the structure of theory via propositions and statistical research via hypotheses run parallel to each other (when, ironically, their prior academic experience has largely ignored this important connection), and (3) how all sciences advance based on probability and outcome models in the decision-sciences through this “mother of all paradigms.” Moreover, if an undergraduate or graduate thesis is around the corner for your students, then an hour’s worth of time on the theory-research connection will be well worth the effort.

One final note, for now. You may wonder if this type of core lecture is better suited for a research methods course (or elsewhere) rather than one in applied statistics. That’s a question only you can answer. Because of the level of specificity I take in my review of the “empirical/observable world,” including non-trivial detail of issues to follow in weeks to come, my approach is best suited for my statistics course. Clearly, you may find such pedagogy useful in a class on theory, research methods, applied statistics or none of the above.

As Craig Ferguson often says when a provocative or controversial idea is raised, “I look forward to your email.”

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### One response to “Conceptualizing the “Core” in Applied Statistics”

1. Hi Drew,

So often in Psychology there is debate over whether we should be teaching research methods first or statistics first, and yet, statistics absent of the context of research, and thus the theory/hypothesis that is driving that research seems too abstract for students to master a statistics.

By looking at your PowerPoint slide it seems that spending a week or two at the beginning of the semester showing students how statistics is applied to testing theories (answering questions), students will be in a better position to more fully grasp the concepts of statistics.

This approach seems very neo- Piagetian, by first assuring that the larger schemata are developed prior to modifying the specific components of those schemata. I would also suspect that such an approach yields greater long term comprehension.

Bonnie