Bioequivalence and Bioavailability Forum

Dear Helmut,

❝ – again.

I am sorry for this gibberish.

Lemme try and explain with a simple made-up case to illustrate my point:
After dosing 4x500 mg of Schützomycin to two random subjects (let's call them Helmut and Detlew for simplicity), I measure how high they can jump. We are interested in knowing the average jump height of these two... erm.. shall we call them 'cases'.
For Helmut I measure (in cm):39,41,51,43,53
For Detlew I measure (in cm):50,39,56,40,42
...and I will now assume IID and blahdeeblahdeeblah and therefore I use a linear model even though jump height presumably cannot be lower than zero and blahblahblah. Let's just do this in R:
Height=c(c(39,41,51,43,53), c(50,39,56,40,42))
Case=as.factor( c(   rep("Helmut",5), rep("Detlew",5)))
Model=lm(Height~0+Case)
 
summary(Model)

Call:
lm(formula = Height ~ 0 + Case)

Residuals:
   Min     1Q Median     3Q    Max
 -6.40  -5.15  -2.90   5.35  10.60

Coefficients:
           Estimate Std. Error t value Pr(>|t|)
CaseDetlew   45.400      3.043   14.92 4.02e-07 ***
CaseHelmut   45.400      3.043   14.92 4.02e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.804 on 8 degrees of freedom
Multiple R-squared: 0.9823,     Adjusted R-squared: 0.9779
F-statistic: 222.6 on 2 and 8 DF,  p-value: 9.712e-08

(let me add: I will of course not fit with an intercept because then the model coefficients are not the LSMeans notch notch wink wink ).

OK, so the two cases seem to perform equally terribly miserably bad under these assumptions for the normal linear model. Lord have mercy. In addition, I see that the residual st error is 6.804 under these circumstances. Aha...
But now I will introduce a game-changer: Let's say I know that the actual Mean for Helmut is 45 and that the actual Mean for Detlew is 47. These are not estimates but true values. Given that I know this, and given our observations, what would then be the most likely residual st error?