Statistical Analysis when the Data is an Image: Eliciting Student Thinking about Sampling and Variability

Margret A. Hjalmarson

George Mason University

mhjalmar@gmu.edu

Tamara J. Moore

University of Minnesota

tamara@umn.edu

Robert delMas

University of Minnesota

delma001@umn.edu

ABSTRACT

Results of analysis of responses to a first-year undergraduate engineering activity are presented. Teams of students were asked to develop a procedure for quantifying the roughness of a surface at the nanoscale, which is typical of problems in Materials Engineering where qualities of a material need to be quantified. Thirty-five teams were selected from a large engineering course for analysis of their responses. The results indicate that engagement in the task naturally led teams to design a sampling plan, use or design measures of center and variability, and integrate those measures into a model to solve the stated problem. Team responses revealed misunderstandings that students have about measures of center and variability. Implications for instruction and future research are discussed.

Keywords: Statistics education research; Statistical modeling; Engineering statistics

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Statistics Education Research Journal, 10(1), 15-34, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), May, 2011

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Margret A. Hjalmarson

Graduate School of Education

George Mason University

4085 University Drive, MSN 4C2

Fairfax, VA 22030