Quantifying and analyzing nonlinear relationships with a fresh look at a classical dataset of student scores

Lingzhi Chen () and Ričardas Zitikis ()
Additional contact information
Lingzhi Chen: Western University
Ričardas Zitikis: Western University

Quality & Quantity: International Journal of Methodology, 2020, vol. 54, issue 4, No 4, 1145-1169

Abstract: Abstract Student past and present performances are analyzed, compared, and reflected upon by teachers, curriculum developers, and educational researchers. For the tasks, methods and techniques of traditional statistics are frequently employed. Recent advances in statistical theory and practice, although not yet covered by widely accessible statistics textbooks, shed additional light on the area and facilitate the improvement of old, and the development of new, curricula that are better aligned with learning goals and outcomes. In the present paper we discuss and illustrate the use of an index of increase that has been designed to quantify, and thus compare, relationships between dependent random variables (e.g., student scores in different study subjects) that rarely follow linear relationships; hence, the use and interpretations of the celebrated Pearson correlation coefficient become problematic. The aforementioned index of increase is the proportion of upward movements among all the movements in the scatterplot arising from paired observations. To appreciate the index from both graphical and mathematical points of view, we have illustrated its performance using a classical and easily accessible educational dataset. We have provided examples of how the index values can aid teachers and educational researchers in determining relationships between student performances in different study subjects, and thus in turn help them in, for example, developing curricula.

Keywords: Educational assessment; Statistical analysis; Dependence; Index of increase; 62P15; 62P25; 91E45; 97C40 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11135-020-00979-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:qualqt:v:54:y:2020:i:4:d:10.1007_s11135-020-00979-7

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/11135

DOI: 10.1007/s11135-020-00979-7

Access Statistics for this article

Quality & Quantity: International Journal of Methodology is currently edited by Vittorio Capecchi

More articles in Quality & Quantity: International Journal of Methodology from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().