Der IQ-Fehler

[1]     Konstrukt :           IQ_x  =  100  + 15 x / σ_x    ;              x    =   ξ    +  δ 

[2]                                                                                            σ²_x  =  σ²_ξ  +  σ²_δ 

[3]     Modell:                 IQ_ξ  =  100  + 15 ξ / σ_ξ    ;               ξ   =   x    -   δ 

[4]                                                                                            σ²_ξ  =  σ²_x  -  σ²_δ 

[5]                                      σ²_ξ  =  σ²_x ρ_xx ;     ρ_xx  =  σ²_ξ / σ²_x

[6]    Konstrukt / Modell             IQ_x  ≤  IQ_ξ     -->          IQ_x    hat Fehler von der Mitte

[7]    praktisch                                  IQ  =  100  + 15 x / σ_ξ 

[8]    allerdings              µ( x / σ_ξ )²  =  σ²x / σ²ξ  ≥ 1  ;    Problem bei  der Normierung (2)