Realization of Zipf's Law in Argumentative Essays by Middle and High School Students

Purpose: This study aimed to investigate whether Zipf's law-a principle explaining various phenomena in nature and human society-is also manifested in the word usage of argumentative essays written by middle and high school students. Methods: A total of 2,362 student essays were analyzed, comprising 894 essays from middle school students and 1,468 from high school students. The frequency of words used in these essays was examined. A visual analysis was conducted to determine whether the word frequency distribution aligns with Zipfian distribution, followed by quantitative validation to verify the conformity with Zipf's law. Results: The word frequency distributions of the entire corpus as well as of each school level approximated Zipf's law. The top 30 words accounted for approximately 40% of the total word occurrences, and the top 10 most frequent words were nearly identical across all three subgroups. Regression analysis, goodness-of-fit tests for power-law distribution, and log-likelihood ratio tests all indicated a strong approximation to Zipf's law. Conclusion: The realization of Zipf's law in student essays reflects a natural linguistic phenomenon governed by the principle of least effort. It also represents a universal pattern emerging from students' efforts to write efficiently while conforming to the topic and argumentative structure. The adherence to Zipf's law in students' writing, despite their ongoing language development, suggests instructional implications for writing and reading education. Teachers may guide students to use a more diverse vocabulary and select reading materials that match students' developmental levels. Furthermore, Zipf's law may serve as a potential benchmark for distinguishing between student-authored texts and those generated by artificial intelligence.