# Focusing on the statistical process

Jill Vanderstoep – Hope College

To be completely honest, I didn’t choose to teach with simulation-based methods. Nathan Tintle made a curricular change, and I followed. To this day, I am so glad I did because the changes have been the most refreshing and fun changes I have made in my Statistics classes over the twenty plus years I have been teaching.

[pullquote]I am so glad I did because the changes have been the most refreshing and fun changes I have made in my Statistics classes over the twenty plus years I have been teaching.[/pullquote]

I always felt like the theory-based introductory statistics course was disjointed and compartmentalized. Our introductory statistics course started with descriptive statistics, then went into probability and sampling distributions, and finally looked at inference for a host of different data types. At the beginning of each semester, I found my students lulled into a state of mind that Statistics was going to be easy and really you didn’t need to allot much study time for it. My students had already seen mean, median, mode, even standard deviation. They had constructed bar graphs, histograms and boxplots in their High School FST (functions/statistics/trigonometry) classes. The first test confirmed my students’ “piece of cake” attitude toward their Statistics class. Many class averages from the first test would be in the low to mid 80s. Then probability and sampling distributions hit. Not something many of the students had seen before. Already in the habit of spending minimal time on their Statistics course, they would find themselves struggling to understand the concepts and how this has anything to do with descriptive statistics. Many of my students would become frustrated and even disengaged at this point in the semester. Test 2 scores plummeted. In the last third of the course, when we would get to the heart of statistics, I would find my students in memorization mode: what formula to use when, what sequence of buttons to push on their calculator, and which rules must be satisfied to make all this valid.

This type of course set up was not what the introductory statistics students needed. In the spring of 2009, Nathan met with me and Todd Swanson to discuss some changes he had been thinking about for the Introduction to Statistics course at Hope College. So I am thinking “Yes, more active learning, better data sets, making more connections between descriptive statistics, sampling distributions and inference, perhaps a focus on student projects.” But Nathan’s vision far exceeded mine. Nathan wanted to start from scratch. We were to embark on a quest for a new curriculum based on simulation and randomization methods, rather than theory-based methods.

The focus of the new curriculum was on the scientific method and the logic and scope of inference.­ The logic of inference looks at weighing evidence to determine whether the study result is statistically significant and then estimating how large the effect of the study result is via confidence intervals. The scope of inference focuses on how the data were gathered. From this we may be able to generalize our results more broadly and possibly make statements about cause and effect. We start this on day one with simulation methods to conduct inference on a single proportion. The simulation-based methods are so intuitive for the students. They understand what just guessing or random chance is. They get that flipping a coin is like guessing between two equally likely outcomes. They see how to model the study under these conditions. When they actually build the null distribution with simulated statistics, they understand why they want to compare their observed statistic to the distribution. They can talk about how few times their observed statistic occurred among all the ones simulated under the just guessing model. If the data aren’t supportive of the model, then the model isn’t a plausible explanation for the study results. The students are engaged in new material from day one. It is at a level they understand and about ideas they are able to discuss among their classmates.

The beginning of the semester is when students are the most excited about learning. Why not capitalize on that? Get the students doing Statistics from day one! Teaching introductory statistics with simulation-based methods has started my students asking questions about randomness, thinking through a statistical study from initial hypotheses to study design to weighing data as evidence, to crafting a conclusion from that evidence and then thinking beyond to what might be a logical follow-up study. I have found my students to be more engaged throughout the course and better able to discuss statistical studies from design to conclusions in a language that a non-statistician can understand. That is what I want my students to be able to do when they leave my class. That is what they are able to do by learning Statistics with simulation-based methods.