Francis Galton - Ahead of His Time

"The senior wranglers [highest scoring students at Cambridge University] had more than thirty, or thirty-two times the ability of the lowest men on the lists of honours. They would be able to grapple with problems more than thirty-two times as difficult; or when dealing with subjects of the same difficulty, but intelligible to all, would comprehend them more rapidly in perhaps the square root of that proportion." (Francis Galton, "Hereditary Genius", 1892, p. 61).

Galton has grasped the concept of separability. The ability of the students is conceptualized separately from the difficulty of any particular set of items, and vice versa.

Understanding Galton's statements in terms of the multiplicative Rasch model, "32 times" = 3.5 logits. In many educational contexts, 1 logit corresponds to one year's growth. So it makes sense that the best-performing students were about 4 years ahead of the worst-performing students.

Andrew Stephanou and colleague

Francis Galton - Ahead of His Time, Andrew Stephanou ... Rasch Measurement Transactions, 2011, 251:2, 1328

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

To be emailed about new material on
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from welcomes your comments:

Your email address (if you want us to reply):


ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website,

Coming Rasch-related Events
April 8-12, 2021, Thu.-Mon. AERA Virtual Conference,
May 21 - June 18, 2021, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 8-11, 2021, Tue.-Fri. NCME Virtual Conference,
June 25 - uly 23, 2021, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),
Aug. 13 - Sept. 10, 2021, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith,Facets),
June 24 - July 22, 2022, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),


The URL of this page is