The mysterious ρ -between or within studies [General Sta­tis­tics]

Dear Nasty!

» So, for ρ=0.8 I get now
» > type1error.2TOST(CV=c(0.3, 0.25), n=122, theta1=c(0.8, 0.9),
» +                        theta2=c(1.25, 1/0.9), rho=0.8, details=TRUE)
» 1e+06 simulations. Time consumed (secs)
»    user  system elapsed
»  979.75   95.18 1115.72
»   Intersection null P(Type I Error) theta0 #1 theta0 #2
» 1      H_A01 n H_Ca        0.048904 0.8000000  0.953047
» 2      H_A02 n H_Ca        0.049193 1.2500000  1.056122
» 3      H_Aa n H_C01        0.049620 0.9709781  0.900000
» 4      H_Aa n H_C02        0.050024 1.0000000  1.111111
» ...

» and inflation at 0.050024

Don't forget, that type1error.2TOST() is based on simulations now.
That's mainly because our (authors team of PowerTOST) brain is to small to derive an analytical solution. And simulations have an error. F.i. in setting the seed for the random number generator.
type1error.2TOST(CV=c(0.3, 0.25), n=122, theta1=c(0.8, 0.9), theta2=c(1.25, 1/0.9), rho=0.8, setseed=F)
[K1] 0.049977

In that light 0.050024 is of course not an alpha-inflation. As we know from theory, the IUT principle, the combination of two TOST via and assures alpha<=0.05. Thus interpret the result as 0.05. Full stop

» As I understand estimated from several datasets ρ is "between studies" ρ while in Power2TOST we need to use "within studies ρ".

I myself don't know what ρ or what value of ρ should be used. As I wrote above: It's under discussion now.

Thus if you or somebody else have an opinion or arguments: Give it to me.

Regards,

Detlew Ing. Helmut Schütz 