?But that's a single CI. If you have n independent CIs, and you want to be 95% confident that they all contain their respective parameters -- i.e., that all n parameters are in the n-dimensional box whose corners are the endpoints of the CIs -- then you must use .95^(1/n), not .95, as the c for each individual CI.?
And I certainly don?t feel I can make a correct decision on which parameters of the design are independent and which aren?t.
Let?s ignore the cS vs cA distinction for the moment, since it will only figure in a secondary thrust of the initial paper (if in fact, any empirically significant difference turns out to distinguish them.) The important member of this pair is cA (because it?s both more accurate and varied), so let?s agree to consider just cA cells.
Next, let?s agree to ignore uA in this discussion, since as you?ve pointed out several times, uA is independent of neither uL nor uH.
So, before considering the regression coefficients themselves, that leaves us with:
a) the six folds a1,a3,b1,b2,c1,v47 b) the uL vs uH dichotomy c) the random vs non-random dichotomy
for a total of 12 independent non-random combinations that can be compared against 12 corresponding random combinations.
Let?s stop there for a moment and consider your ?n parameters in the n- dimensional box?. Do (a-c) imply an n of 24 or an n of 12? (Or am I seeing this entirely wrong-headedly, and n is something else here.)
Now let?s go to the 7 regression coefficients:
eS eI uS uI euS(e) euS(u) eu(I)
Of the 7 x 7 possible pairs of these coefficients, you?ve already pointed out a number that aren?t independent, e.g. eS and euS(e) or uS and uS(u). Similarly, I assume that eS and eI are not independent, nor uS and uI.
But what is the complete inventory of independent parameters based on the regression coefficients we?re considering? Whatever that number is, I assume we multiply that by whatever inventory you derive from (a- c).
But again, I have no idea whether I?m even remotely thinking about this in a correct way, so please advise what you think n should be (and why, if you have the time.)