Das echte    g,1-Faktor-Modell

                                        (nach welchem SPEARMAN gesucht hatte)

Konstrukt      

                         [1]           1_y  =  G_y  + Rest

                                                   G_y:= Generalfaktor    THURSTONE, SPEARMAN

Modell         [2]           1_y   =  g_y² + E_y ;             g_y² = ρ_yy ,     E_y = σ²_ε / σ²_y                   

Die Ertweiterung der  CAUCHY-SCHWARZ` en  Ungleichung

[3]         σ_yx     ≠  σ_y σ_x ,           µ(yx = ηξ + ηδ +ξε + εδ)   = σ_ηξ  ;       y = η+ε ,  x = ξ+δ

[4]         σ_yx   =  σ_ηξ                ^         σ_ηξ  =  signσ_ηξ  σ_ησ_ξ          -->          σ_yx  =  signσ_xy  σ_ησ_ξ 

[5]                           ( signσ_xy   =  signσ_ξη  =  ± 1 ) ,                                      σ_yx ²  =  σ²_ξ*σ²_η     

 [6]   Modell                     

 [7]                             ρ_xy    =  a_xI*a_yzI ,        g  := aI  ,         

 [8]                             ρ_xy   =  signσ_yx (σ_ξ/σ_x)(σ_η/σ_y) = σ_xy/σ_xσ_y ,   (4)  (7)  

                           ρ_xz, ρ_yz   = analog

[9]                            ρ_xy   = g_x g_{y  ,}          |g_x|   =    σ_ξ / σ_x  = (ρ_xx)^1/2

                                                                  |g_y|  =   σ_η / σ_y  = (ρ_yy)^1/2

[10]                           ρyy = a²_yI      und analog