When I am attempting to test understanding of carrying out a simulation test about a single proportion, I like to use the following problem, or some variation of it. I’m fond of animals and studies that show that animals are clever, so this study and ones like it, appeals to me.
A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in 7 of 8 scenarios that she was presented. In order to judge whether Sarah understands how to solve problems we will define π to be the probability Sarah will pick the photo of the correct solution.
I don’t let them get away with just claiming that the p-value is some particular number – they have to explain how they know it is that number.
One of the biggest challenges we all face as teachers of statistics is testing students’ statistical knowledge. For example, how do we know if the assessment questions we write are assessing students’ understanding of the statistical material and not some irrelevant construct? How do we know how many questions should be on an assessment to truly see if students are “getting it?” But these questions are only the tip of the iceberg. I know we also grapple with finding interesting contexts and datasets for assessing a particular statistical method; It is hard and time consuming! I have often found an exciting example and dataset only to find that once I start digging into the data, it is beyond the level expected of my introductory statistics students (*Sigh…back to the drawing board). When I was asked to write this blog post, I thought it would be great to share an interesting question so that the task of assessment development isn’t so burdensome for others.
I think it is important to note that I am not just asking them to conduct a randomization test, but am also asking them for interpretations and to think about how study design affects our conclusions. Asking them a multitude of questions for one context also saves me time for coming up with different contexts and reduces cognitive load for my students.