## Calculation of intra-subject CVs in replicate design [General Sta­tis­tics]

Hello David,

i agree with your assignment of the intraindividual error terms.

❝ Covariate Parameter Estimates

❝ Cov Parm Subject Group Estimate

❝ FA(1,1) Subject 0.5928 <---- (sig_BT, the between-subject standard

❝ deviation for the Test product)

❝ FA(2,1) Subject 0.4968 <---- (sig_BR, the between-subject standard

❝ deviation for the Reference product)

❝ FA(2,2) Subject 2E-17 <---- (sig_D, the subject-by-formulation

❝ interaction term)

But your assignment of the FA(i,i) terms to the interindividual (co)variances is not correct i think.
Think of the G matrix (using your notation):
    G(1,1) = sig_BT2    G(2,2) = sig_BR2    G(1,2) = rho*sig_BT*sig_BR

Futher it is defined (subject-by-formulation interaction variance)
    sig_D2=G(1,1)+G(2,2)-2*G(1,2)          =sig_BT2+sig_BR2-2*rho*sig_BT*sig_BR 
The FA0(2) parameterization of the G-Matrix reads
    G(1,1)=FA(1,1)2    G(2,2)=FA(2,1)2+FA(2,2)2    G(1,2)=FA(1,1)*FA(2,1)

Confer to the SAS documentation for this.
By the way: G(1,1) = sig_BT2 is only valid, if your coding of test treatment preceedes that of the reference.

Thus with some algebra you obtain
    FA(1,1)=sig_BT    FA(2,1)=rho*sig_BR    FA(2,2)=sqrt(1-rho2)*sig_BR 

Thus your assignment of FA(2,1) is only valid if rho=1 which implies FA(2,2)=0.
In that case the subject-by-formulation interaction variance is
   sig_D2=FA(1,1)2+FA(2,1)2-2*FA(1,1)*FA(2,1) 

Regards,

Detlew  Ing. Helmut Schütz 