My move from the traditional curriculum to the simulation/randomization-based curriculum was confounded with the simultaneous move of inference to the beginning of the course. Not only was I going to dive in to simulation/randomization as the primary mode by which to develop student understanding of statistical significance, but I was going to try it while completely turning the traditional ordering on its head.
But moving inference to week 2 means my students immediately experience statistics as a science, and they get this experience repeatedly throughout the course, and in the end showing them what statisticians do and how statisticians think is more important than my struggle with where to put the definitions of parameter and statistic.
While this was a tall order and perhaps fraught with difficulty, I found that using simulation/randomization-based methods was the easy part. In comparison, moving inference to week 2 of a 10-week quarter was actually the hard part. Why was the switch from traditional to simulation easy? Certainly it took more work and preparation on my part. And for the introduction of inference, letting go of all the notation and formulae of hypothesis testing was intimidating, but from a student perspective it’s intuitively appealing. Once students understand that simulation can be used to determine probabilities in the long-run sense, what better way to assess how surprising a study outcome is than by comparing that outcome to what could happen by random chance?
On the other hand, what makes moving inference to the beginning of the quarter so difficult? In the traditional curriculum the foundations are laid before arriving at hypothesis testing. Students have already seen what descriptive statistics are, what we mean by variability and how to summarize data, what random samples are and why they are important. In addition, they have covered the fundamental language of statistics, basic ideas such as population, parameter, variable, and statistic. Beginning the discussion of inference so early means this language and these foundational ideas have not been fully developed. They are taught as they are needed, just-in-time. Thus, students can grasp the idea of studies having two potential explanations (random chance vs. the research conjecture), and they can assess the statistical significance of a study result by simulation to obtain a p-value, but these concepts may get lost or minimized as the students struggle to understand why a symmetric bell-shaped histogram is centered at its mean.
After teaching this way for eight quarters, I still struggle with the just-in-time paradigm, but I am whole-heartedly on board with the simulation/randomization-based curriculum. I recognize that one simple solution would be to preserve the traditional ordering of topics and use simulation/randomization to introduce inference later in the quarter. But moving inference to week 2 means my students immediately experience statistics as a science, and they get this experience repeatedly throughout the course, and in the end showing them what statisticians do and how statisticians think is more important than my struggle with where to put the definitions of parameter and statistic.