[R] Help with Post-Hoc tests for TWO-WAY within subject ANOVA

From: Xiao He <praguewatermelon_at_gmail.com>
Date: Wed, 09 Jun 2010 22:04:47 -0700


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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