The concept of IRT (Item Response Theory), offering several models which at least guarantee if they hold, that a scoring rule in question is indeed fair, can be referred to in regard to the pertinent scoring rule of the IQ (intelligence quotient) in many intelligence test-batteries. Muller's continuous Rasch model (1987, 1999) applies. Analyses were carried out for three test-batteries, that is the German and the English version of AID 3 and a respective version for group administration, to show this in an exemplary way. Sample sizes comprised 431, 761, and 2278, respectively. Above all, the graphical model check disclosed a serious misfit of the model: There is no support for the notion that the respective scoring rule is fair. Detailed inspections give the impression that essentially calculating the sum of the subtest scores mixes (at least) two components, "intelligence" and "willingness to achieve in unchallenging tasks." Practitioners should be assailed by doubts that all other intelligence test-batteries in use, which are not evaluated accordingly, do score fair.