Statistics students' identification of inferential model elements within contexts of their own invention

TL;DR

This study investigates how post-secondary students identify key elements of statistical models in their own invented contexts, revealing strengths in recognizing samples and populations but challenges with statistics and parameters.

Contribution

It introduces an alternative assessment task prompting students to identify model elements in self-created contexts, highlighting areas for instructional improvement.

Findings

Students accurately identified sample and population.

Responses for statistic and parameter were less reliable.

Many responses confused variables or study design details with model elements.

Abstract

Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original problem setting (Wild and Pfannkuch 1999). Assessment in introductory statistics often relies on tasks that present students with data in context and expects them to choose and describe an appropriate model. This study explores post-secondary student responses to an alternative task that prompts students to clearly identify a sample, population, statistic, and parameter using a context of their own invention. The data include free text narrative responses of a random sample of 500 students from a sample of more than 1600 introductory statistics students. Results suggest that students' responses often portrayed sample and population accurately. Portrayals of statistic and parameter were less reliable and were associated with descriptions of a wide variety of other concepts. Responses frequently attributed a variable of some kind to the statistic, or a study design detail to the parameter. Implications for instruction and research are discussed, including a call for emphasis on a modeling paradigm in introductory statistics.