Abstract
Grade point averages (GPAs) are calculated by assigning numbers to letter grades and averaging them. Simple examples show that the method cannot consistently determine class rank since class rank is sometimes permuted with arbitrary change of scale. This permutation is only possible when one student is somewhere worse and somewhere better than a second. The distinction between these and other sorts of cases is established by theorems proved in an appendix. Relativistic attempts to resolve the inconsistency are shown to be insufficient. The function of GPAs as predictors is briefly discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Arrow, Kenneth J. (1951). Social Choice and Individual Welfare. Cowles Commission Monograph 12. New York: John Wiley and Sons.
Lang, David M. (1997). Accurate and Fair Class Ranks: One Step Closer with the Class Rank Index, ERS Spectrum 15(3) (Summer 1997): 26–29.
Milton, Ohmer, Pollio, Howard R., and Eison, James A. (1986). Making Sense of College Grades: Why the Grading System Does Not Work and What Can be Done About It. Foreword by Laura Bornholdt. San Francisco and London: Jossey-Bass Publishers.
Siegel, Judith, and Anderson, Carolyn S. (1991). Considerations in Calculating High School GPA and Rank-in-Class. NASSP Bulletin 75(537) (October 1991): 96–109.
Simpson, E. H. (1951). The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society series B 13: 238–241.
Suppes, Patrick, and Zinnes, Joseph L. (1963). Basic measurement theory. In R. Duncan Luce, Robert R. Bush, and Eugene Galanter (eds.), Handbook of Mathematical Psychology, vol. I. New York and London, John Wiley and Sons.
Young, John W. (1990). Are validity coefficients understated due to correctable defects in the GPA? Research in Higher Education 31(4): 319–325.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vickers, J.M. Justice and Truth in Grades and Their Averages. Research in Higher Education 41, 141–164 (2000). https://doi.org/10.1023/A:1007069620329
Issue Date:
DOI: https://doi.org/10.1023/A:1007069620329