In trying to clear out my e-mail inbox, I came across this post, for
which there seemed not to have been any responses.
On Fri, 2 Feb 2001, Caroline Brown wrote:
> I have an analysis problem, which I am researching solutions to, and
> David Howell of UVM suggested I mail the query to you.
> My problem is how to deal with a two way- repeated measures design,
> in which one cell could not be measured:
> A1 A2 A3
> B1 ok ok ok
> B2 - ok ok
> B3 ok ok ok
> B4 ok ok ok
>
> There is a good theoretical reason for this absence, as levels of
> factor A are set sizes, and A1 is one item, Factor B is cueing to
> spatial location and in the 1 item set size, there are no other items
> competing for 'encoding' resources (thus there can be no INVALID cue).
>
> If you know of any texts or papers on this issue, or have any thoughts
> as to its solution, I would be most grateful.
One approach is to estimate the cell mean in the A1B2 cell, under the
constraint that it not contribute to the AxB interaction; and then
carry out the usual 2-way ANOVA (but with one fewer d.f. for
interaction).
If we use the following two contrasts, one for main effects in A and one
for main effects in B, their product represents a contrast involving the
12 cells. Set that contrast equal to zero (so it doesn't contribute to
the interaction SS. (All other interaction contrasts orthogonal to this
one will not involve the missing cell.)
For A: 2A1 - A2 - A3. For B: -B1 + 3B2 - B3 - B4. Product contrast:
-2A1B1 + A2B1 + A3B1 + 6A1B2 - 3A2B2 - 3A3B2
- 2A1B3 + A2B3 + A3B3 - 2A1B4 + A2B4 + A3B4 = 0, whence
A1B2 = (2A1B1 - A2B1 - A3B1 + 3A2B2 + 3A3B2 + 2A1B3 - A2B3 - A3B3
+ 2A1B4 - A2B4 - A3B4)/6
(where "2A1B3" = twice the cell mean in the (A1,B3) cell, etc.)
You now have cell means for each cell and can carry out the usual ANOVA.
Because the estimated value of A1B2 infects your A1 average and your B2
average, the row and column effects (sources "A" and "B" in the ANOVA)
are not, strictly speaking, independent; although the A2:A3 contrast is
independent of contrasts involving only B1, B3, B4.
Hope this helps (if belatedly!).
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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