Dear R users,

I posted a couple of questions and got no response, so I am giving it
another shot.

I ran an experiment with a TWO-WAY within subject design. A sample dataset
is in http://www-scf.usc.edu/~hex/data.txt

I already ran ANOVA by using the following formula:

aov(RT~Factor1*Factor2 + Error(Subject/(Factor1*Factor2)), data=data)

and I obtained the following information:

-------------

Error: Subject

               Df  Sum Sq Mean Sq F value Pr(>F)

Residuals 19 6154709  323932



Error: Subject:Factor1

               Df  Sum Sq Mean Sq F value Pr(>F)

Factor1      1  131017  131017  1.2624 0.2752

Residuals 19 1971836  103781



Error: Subject:Factor2

                Df  Sum Sq Mean Sq F value Pr(>F)

Factor2      1   48042   48042  0.4281 0.5207

Residuals 19 2132016  112211



Error: Subject:Factor1:Factor2

                        Df  Sum Sq Mean Sq F value  Pr(>F)

Factor1:Factor2  1  500137  500137  7.3702 0.01374 *

Residuals          19 1289336   67860

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Error: Within

           Df   Sum Sq Mean Sq F value Pr(>F)

Residuals 560 54063256   96542
----------------

Now my question is, what kinds of post-hoc tests can be used to examine
which of the 4 conditions generated by the 2X2 design is different. From the
research I did online, I found that TukeyHSD cannot be used because the
aov() function I used contains random effects. I also read that
pairwise.t.test adjusted with the Bonferroni method is not good either
because it assumes that the null hypothesis is not rejected, hence
overcorrecting TYPE 1 error. It would be great if someone could shed some
light on my problem. Thank you in advance!


Xiao

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