"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
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