With the green light to make as dramatic a proposal as I desired, I set to considering a new syllabus accompanied by general learning objectives in February 2019. My guiding principles were based on what I had recently learnt about statistics education research, my experiences teaching HSCI 2117, and my experience working as a statistician in the health sciences. I knew I wanted to make decisions supported by academic research, but before I went hunting for recommendations in the research literature, I sat down to plot out where my current visions lay.
New statistical reasoning course objectives
I wanted my students to walk out of my course with knowledge and skills that would allow them to use data to inform decisions. This meant I needed them to be comfortable asking a question, collecting relevant data, summarizing and describing data, and using data to make inferences. Specific modules could focus on:
- measurement – focusing on validity and data collection
- types of variables (categorical, ordinal, discrete quantities, continuous ratio scales) – the backbone to future instruction, as each of the tools I would introduce can be mapped to a subset of these four types in univariate and bivariate cases
- summary statistics and data visualizations
- modelling – focusing on ‘naming’ identified patterns from summaries and descriptions
- inference – focusing on sampling variability, likelihood as a measure, and interval estimation
- hypothesis testing – introducing both null hypothesis testing and also comparing two hypotheses or models in significance testing
While this helps me to decide on content, the specific reasoning skills that I could stress would be reasoning about data, reasoning about variability, and reasoning about inference. While we do touch on modelling, I feel that models and modelling require too much attention to include in addition to setting a solid foundation for inference in general.
Out with the old and in with the new
Furthermore, the manner in which I wanted to teach these materials was vastly different from the old standard curriculum. It is 2019 – I do not need my students to know how to use a normal probability table. No one does that any more. As such, I decided on the following changes in content:
- Exclude by-hand calculations – Although one could argue that working out equations is the only way to truly understand them, I wanted this course to be a statistical literacy course. What real value is there in having a student being able to calculate the standard deviation of a dataset by hand? I believe the answer is ‘none’.
- Exclude probability theory and probability distributions – I knew this was a recommendation of GAISE 2016, and it was something that students often struggled with. In the consensus curriculum, I think its introduced in order to facilitate calculations of test statistics by hand, a need now obviated.
- Exclude the critical value approach and tests statistics – although understanding sampling distributions is arguably an essential aspect of statistical literacy, I do not believe it is worth the trouble in an undergraduate introductory course. It is more important to develop students’ understanding of sampling variability, which can be done without specifically addressing sampling distributions at all. Since in practicing statisticians rely on p-values and confidence intervals, I decided to go with a combination of the p-value and the confidence interval approach, further diminishing value in introducing critical values and test statistics.
- Exclude the one-sample Z-test for a proportion and the two-sample Z-test for a difference in proportions – these tests are approximations of exact tests and were prevalent in an age before computers. If we are adopting a p-value and confidence interval approach, then the choice of the test we instruct is irrelevant. Why not just teach the exact tests?
Preparing for the hunt for a new text book
Satisfied with my proposed changes, I thought about how I would operationalize instruction for each of my major learning objectives, began to search for a new text book that would align with these values.
References and further reading:
GAISE (2016). Guidelines for assessment and instruction in statistics education. College report. Alexandria, VA: American Statistical Association
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer Science & Business Media.