This is a question only about terminology.
Suppose I have data categorized by three factors A, B, and C, with cell means
ybar_ijk and cell frequencies n_ijk, where I, j, and k index A, B, and C
respectively. And suppose I want to summarize the results for factor A by
computing some sort of weighted means WM_i, averaging over indices j and k with
weights w_jk. Consider these four weighting schemes:
1. Use equal weights, w_jk = 1
2. Use weights of w_jk = n_+jk (where "+" shows I summed over
that index)
3. Use weights w_jk = n_+j+ * n_++k (outer product of the one-factor
marginal frequencies)
4. Use weights w_ijk = n_ijk (only one where we use a different set of
weights for each i)
Scheme 1 yields the "unweighted" or "least-squares" means,
and scheme 4 yields the ordinary means for A, ignoring B and C altogether.
Scheme 3 yields weighted averages over k of weighted averages over j (or vice
versa).
My question is what to call these schemes, e.g., as a character argument in an R
function. Preliminarily, I am calling them "equal",
"proportional", "outer", and "actual". The first
one is pretty obvious. But maybe there is some existing standard terminology for
some or all of the others that I am unaware of (or have forgotten). Any
suggestions?
Russ
Russell V. Lenth - Professor Emeritus
Department of Statistics and Actuarial Science
The University of Iowa - Iowa City, IA 52242 USA
Voice (319)335-0712 (Dept. office) - FAX (319)335-3017