Percentile-difference scales are crude and embody a fundamental fallacy because percentile units are not equal intervals¶

Claim · All claims
Evidence · 1 study (2 entries) · design r1 · q1
Currency · newest study 1915 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q1 i? The article argues that scales built on percentile differences are crude and fallacious, and that raw percentile values from different tests cannot be equated, translated or combined. → Wells 1915 q1 i? Adjacent percentile intervals differ in size, unlike equal-unit scales: the gap between the 0th and 10th percentiles is not equal to the gap between the 50th and 60th. → Wells 1915 (2)

Evidence¶

Wells 1915¶

Wells, G. R. (1915). An apparatus for the mirror-drawing test; Percentile norms for scaling data. Journal of Educational Psychology. https://www.google.com/search?q=%22An+Apparatus+for+the+Mirror-Drawing+Test%22

q1 · i? · design · r1

A theoretical argument (type e) about scaling practice, offered without data. The article adds that the significance of, for example, the 80th percentile varies with the variability and dispersion of different traits.

"Scales devised upon a basis of percentile differences are bound to be very crude, besides embodying a fundamental fallacy."

Wells 1915 (2)¶

Wells, G. R. (1915). An apparatus for the mirror-drawing test; Percentile norms for scaling data. Journal of Educational Psychology. https://www.google.com/search?q=%22An+Apparatus+for+the+Mirror-Drawing+Test%22

q1 · i? · design · r1

The article's illustration of unequal percentile intervals, contrasted with scales in which "the difference between points 5 and 6 on our scale is equal to the difference between 0 and 1". The text is truncated at this point.

"The difference between the 0 and the 10th percentiles is not equal to the difference between the 50th and 60th or between the 70th or"

Discussion¶

Related Claims¶

• The two test forms were built to pair exercises of closely the same value, equal total values, and similar inter-exercise intervals, with 100 total points per form — related
• The Organization Test exercises were scaled on 1634 children in grades three to eight, yielding difficulty values from .03 to 6.4 units — related
• Against Stanford Binet criteria for 300 grade 3–6 children, the mental index correlated .47, the educational index .52, crude score with mental age .80, mental with educational index .62, and Difference with I.Q. .21 — related
• Scaling is a sine qua non for experimental use of tests, and unscaled tests interpreted as scaled do harm — a narrower finding that bears on this claim