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Benford's Law: textbook exercises and multiple-choice testbanks
Aaron D Slepkov1, Kevin B Ironside1, David DiBattista2
1Department of Physics & Astronomy, Trent University, Peterborough, Ontario, Canada.
Plos One
|February 18, 2015
Summary
Benford's Law, a digit distribution pattern, was observed in textbook answers for physics and chemistry. While the answers followed this pattern, it did not provide an advantage for guessing on multiple-choice tests.
Area of Science:
- Scientific data analysis
- Educational assessment
Background:
- Benford's Law details the non-uniform distribution of leading digits in many real-world datasets.
- This law is commonly used for fraud detection in financial and accounting data.
- The applicability of Benford's Law to educational datasets was previously unexplored.
Purpose of the Study:
- To determine if answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford's Law.
- To investigate if this conformity can be exploited to gain an advantage in multiple-choice tests.
Main Methods:
- Collected leading digit data from answers in physics and chemistry textbook exercises.
- Analyzed the distribution of these digits using Benford's Law criteria.
- Evaluated the potential for exploiting digit distribution in multiple-choice test scenarios.
Main Results:
- Leading digits of answers in physics and chemistry textbook exercises conform to Benford's Law.
- Introductory physics testbank answers closely follow Benford's Law distribution.
- Despite conformity, the testbank was secure against a Benford's Law-based guessing strategy.
Conclusions:
- Benford's Law applies to numerical answers in science textbooks.
- Conformity to Benford's Law does not necessarily create a vulnerability in multiple-choice tests.
- The distribution of answers, while predictable, does not offer a practical advantage for test-takers.