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I have performed a repeated measures ANOVA in R, as follows:

aov_velocity = aov(Velocity ~ Material + Error(Subject/(Material)), data=scrd)
summary(aov_velocity)
  • What syntax in R can be used to perform a post hoc test after an ANOVA with repeated measures?
  • Would Tukey's test with Bonferroni correction be appropriate? If so, how could this be done in R?
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    $\begingroup$ see this related question on post hoc tests for repeated measures designs stats.stackexchange.com/questions/575/… $\endgroup$
    – Jeromy Anglim
    Commented Aug 11, 2011 at 10:08
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    $\begingroup$ About your 2nd point: Tukey's HSD already includes a "correction" for multiplicity (at the level of the test statistic, not the alpha level like in Bonferroni's method). So, there's no need to combine both. $\endgroup$
    – chl
    Commented Aug 11, 2011 at 11:35
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    $\begingroup$ @chl: so we don't need to correct the alpha level during the multiple pairwise comparisons in the case of Tukey's HSD ? $\endgroup$
    – abc
    Commented Sep 26, 2011 at 3:46
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    $\begingroup$ @stan No. (Note: Unplanned (post-hoc) tests should be performed after the ANOVA showed a significant result, especially if it concerns a confirmatory approach.) $\endgroup$
    – chl
    Commented Sep 26, 2011 at 8:15
  • $\begingroup$ I cannot find the data scrd to run the example $\endgroup$
    – Dimitrios Zacharatos
    Commented Feb 3, 2020 at 11:30

3 Answers 3

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What you could do is specify the model with lme and then use glht from the multcomp package to do what you want. However, lme gives slightly different F-values than a standard ANOVA (see also my recent questions here).

lme_velocity = lme(Velocity ~ Material, data=scrd, random = ~1|Subject)
anova(lme_velocity)

require(multcomp)
summary(glht(lme_velocity, linfct=mcp(Material = "Tukey")), test = adjusted(type = "bonferroni"))

For other contrasts then bonferroni, see e.g., the book on multcomp from the authors of the package.

You may also want to see this post on the R-mailing list, and this blog post for specifying a repeated measures ANOVA in R.

However, as shown in this question from me I am not sure if this approachs is identical to an ANOVA. Furthermore, glht only reports z-values instead of the usual t or F values. This seems to be uncommon, too.

So far, I haven't encountered another way of doing this.

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If you want to stick with the aov() function you can use the emmeans package which can handle aovlist (and many other) objects. 

library("emmeans")
# set orthogonal contrasts
options(contrasts = c("contr.sum", "contr.poly"))

aov_velocity <- aov(Velocity ~ Material + Error(Subject / Material), data = scrd)

After creating an emmGrid object as follows

emm <- emmeans(aov_velocity, ~ Material)

it is very easy to get all (post hoc) pairwise comparisons using the pairs() function or any desired contrast using the contrast() function of the emmeans package. Multiple-testing adjustments can be achieved via the adjust argument of these functions:

pairs(emm)  # adjust argument not specified -> default p-value adjustment in this case is "tukey"

For more information on this I found the detailed emmeans vignettes and the documentation to be very helpful.

Also, you can find a complete (reproducible) example including a description on how to get the correct contrast weights in my answer here.

Note, however, that using a univariate model for the post hoc tests can result in anti-conservative p-values if sphericity is violated.

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If sphericity is met then you can run a two-way ANOVA: 

aov_velocity = aov(Velocity~Material+Subject, data=scrd)
posthoc      = TukeyHSD(aov_velocity, 'Material', conf.level=0.95).
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