## SE of ∆ [General Sta­tis­tics]

Dear Helmut,

❝ ❝ BTW: the formula (2) is not the error term in the 2×2×2 crossover.

❝ How would you call it?

See the subject of your post.
The error term in the 2×2×2 crossover is MSE (aka mean squared error). Or the square root of MSE.

❝ We use $$(3)$$ in PowerTOST’s BE_CI.R line 30:

sqrt(mse*ades$bkni*nc) where for design = "2x2" ades$bkni is 0.5 and nc is sum(1/n[1]+1/n[2]).

❝ If we agree that $$\small{\widehat{\sigma}_\textrm{w}=\sqrt{MSE}}$$ * we end up with $$(2)$$

Correct.

Regards,

Detlew