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I run a two-way repeated measures anova in R:

a<-aov(acc~sound*cnd + Error(sbj/(sound + cnd)), data=d)

I regressed accuracy (of participants, sbj) on cnd (condition, having two levels: abstract vs. environmental), and sound (having four levels: 1st,2nd,3rd,4th). There is an interaction, so I analysed data from each condition separately. Results were similar in both conditions: There was an effect of sound, and post-hoc comparisons (following this post) suggested these differences : (1st)>(4th)> (2nd or 3rd), for both conditions, as can also be seen on the graph below: enter image description here

But the interesting part in my results is the interaction.

My question is how can I compare the differences between conditions at each level of sound.

I have already used package emmeans, so I managed to see that the difference is significant for each level of sound.

m<-emmeans(a, ~cnd|sound)
pairs(m)

But this not what I am looking for. I need to conduct multiple comparisons on the differences between means. To be more clear(please see the image), I need to check if a and d are greater to b and c.

Any ideas?

Any suggestion would be greatly appreciated.

Fotis

fotisfotiadis
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  • You need a contrast of contrasts. so save the first set of contrasts and contrast them: con <- pairs(m); contrast(con, list(ab.vs.cd = c(1,1,-1,-1)/2), by = NULL) – Russ Lenth Jul 28 '20 at 23:24
  • Thanks Russ. But I need to do all six comparisons, namely: a vs, b, a vs. c, a vs. d, b vs. c, b vs. d, c vs. d. Not just compare a+d vs. c+d (I should have been more clear). Any thoughts? – fotisfotiadis Jul 29 '20 at 07:10
  • That isn't what you asked, but it's even easier: pairs(con, by = NULL). Or contrast(m, interaction ="pairwise", by =NULL). This stuff is all pretty well documented. Please read the vignetter on interactions. – Russ Lenth Jul 29 '20 at 12:30
  • Russ, thank you so much for the response, that was exactly what I was looking for. I really appreciate your advice! (And I will read the vignetter you suggested). Regards – fotisfotiadis Jul 29 '20 at 18:38
  • One more question please, regarding multiplicity adjustments. I need to do another post-hoc test. Namely, I need to check if consecutive differences between sounds are different among conditions. So, I first calculated differences for each conditions, m2<-emmeans(a, ~sound|cnd), and then consecutive contrasts, con2<-contrast(m2, "consec"). Now, what I finally need are these comparisons: pairs(con2, by="contrast"). But the output suggests that these are 3 independent tests. Right? Any way that the 3 comparisons are adjusted for multiplicity? Thank you again – fotisfotiadis Aug 15 '20 at 09:49
  • Yes. You need to null-out the by variable and summarize -- summary(pairs(con2, by = "contrast"), by = NULL, adjust = "mvt") – Russ Lenth Aug 15 '20 at 12:24
  • Thank you again, prof. Lenth. Your help is much appreciated! – fotisfotiadis Aug 15 '20 at 14:00

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