Greetings.
I am not totally sure where to post this query so forgive me if this is the
wrong SIG. However, I do teach stats in conjunction with experimental design
and the question is one that is of considerable interest right now to several
of my grad students and myself - hence this presents a weak rationale for
sending the query to this listserv.
As background, I am very familiar with Type III marginal SS for ANOVAs.
However, we have a situation where a reviewer is insisting on an analysis that
requires thin slicing our data so that we do not have observations in some of
the cells for some of our Ss. I think I understand what R is telling me, but I
am not positive that I do. Even worse, I don't know how to explain the analysis
(assuming I have interpreted it correctly) to the editor or to the readers of
the journal who, like me, are familiar with Type III ANOVAs.
I have tried to attach the R file plus the data file to this email. I am not
sure whether the listserv will allow attachments. If not these files can be
found here:
Rcode: files.me.com/graywayne/7z7db3
data: files.me.com/graywayne/688878
What I think is the "takeaway" point is that there is no evidence in our data
that the factor "dens.targ" is significant or that any of its interactions are
significant. Given that the other analyses strongly support our interpretation
of the results, I would like to conclude that any effect of density of the
target stimuli on response time is very weak at best. This is a very
satisfactory conclusion to me, however, I want to go the extra mile to show the
editor that we tested this as best we could. Although it might appear in the
paper, it is not clear that it would. It may be the sort of thing you do to
present to the Editor but leave out of the final version of the paper.
Any help, comments, pointers, etc will be much appreciated.
BTW: This is a visual search paradigm where the factor of interest is the
density of distractors in the quadrant in which the target is found. The data
are limited to those cases in which the initial visual saccade is to a "dense
quadrant" or a "nondense quadrant" for those cases in which the initially
saccaded-to-quadrant also contained the "target." The DV, TRIAL.TIME, is the
time from the beginning of the trial to the point where the subject indicates
they have found the target by clicking a key.
Yours,
Wayne Gray
> anova.e1sq <- with(e1sq, summary(aov(TRIAL.TIME ~ BLOCK.NUMBER*dens.targ +
> Error(SUBJECT/(BLOCK.NUMBER*dens.targ)))))
> anova.e1sq
Error: SUBJECT
Df Sum Sq Mean Sq F value Pr(>F)
BLOCK.NUMBER 3 9237318 3079106 0.9906 0.5030
dens.targ 1 8661 8661 0.0028 0.9612
BLOCK.NUMBER:dens.targ 3 254237 84746 0.0273 0.9927
Residuals 3 9324782 3108261
Error: SUBJECT:BLOCK.NUMBER
Df Sum Sq Mean Sq F value Pr(>F)
BLOCK.NUMBER 3 2516104 838701 1.4333 0.2557
dens.targ 1 166064 166064 0.2838 0.5987
BLOCK.NUMBER:dens.targ 3 362702 120901 0.2066 0.8909
Residuals 26 15213849 585148
Error: SUBJECT:dens.targ
Df Sum Sq Mean Sq F value Pr(>F)
dens.targ 1 272316 272316 2.4674 0.1602
BLOCK.NUMBER:dens.targ 3 404184 134728 1.2207 0.3710
Residuals 7 772557 110365
Error: SUBJECT:BLOCK.NUMBER:dens.targ
Df Sum Sq Mean Sq F value Pr(>F)
BLOCK.NUMBER:dens.targ 3 367036 122345 0.9171 0.4444
Residuals 30 4002169 133406
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 418 59572437 142518
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