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In my linear mixed effects model, I had a significant interaction, I followed up the interaction with orthogonal contrast codes to see where the difference was.

How do I report my findings, other than a p-value? Do I need to report a t or F statistic as well?

 Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF  DenDF  F value    Pr(>F)    
group                      3566    1783     2  90.01   1.0697   0.34743    
session                   30588   30588     1 629.03  18.3504 2.125e-05 ***
trialtype               3004359 1001453     3 629.03 600.7995 < 2.2e-16 ***
group:session             13907    6953     2 629.03   4.1715   0.01586 *  
group:trialtype            6066    1011     6 629.03   0.6065   0.72522    
session:trialtype         11775    3925     3 629.03   2.3547   0.07094 .  
group:session:trialtype    6154    1026     6 629.03   0.6153   0.71815

For the contrast code, I left the last two as all 0s because I was only interested in compared Group 1 pre-post (1-4) Group 2 pre-post (2-5) and Group 3 pre-post (3-6). Please correct if this is wrong.

contrastmatrix<-cbind(c(1,0,0,-1,0,0),c(0,1,0,0,-1,0),c(0,0,1,0,0,-1),c(0,0,0,0,0,0), 
                  c(0,0,0,0,0,0))
contrasts(pairwisegp)<-contrastmatrix

summary.lm(aov(rt~pairwisegp))

Coefficients: (2 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  302.910      3.588  84.429   <2e-16 ***
pairwisegp1    5.431      6.210   0.875   0.3821    
pairwisegp2    2.016      6.223   0.324   0.7460    
pairwisegp3   12.373      6.210   1.993   0.0467 *  
pairwisegp4       NA         NA      NA       NA    
pairwisegp5       NA         NA      NA       NA  
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    $\begingroup$ It would help a lot to see a copy of the results summary, to see the evidence for the interaction and to clarify what you mean by "I followed up the interaction with orthogonal contrast codes to see where the difference was." Please edit your question to provide that information. $\endgroup$ – EdM Aug 13 at 19:48
  • $\begingroup$ @EdM thank you, I updated the post $\endgroup$ – CogNeuro123 Aug 13 at 19:58
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For the first part of your question, reporting p values by themselves provides little useful information. This thread is a good introduction to the limits, even the dangers, of relying on p values.

A reader is going to want to know details about the size of the sample on which the results are based, the magnitudes of individual effects, of differences among treatments, and a measure of potential errors in those estimates. The point estimates and associated confidence intervals of effects or differences among treatments are thus most important. See this thread for related discussion.

For the second part of your question, it seems that you might have moved from a mixed model in your first code block (assuming this is related to your other post, which shows a random effect for subjects) to a fixed model in the second code block. I guess this because you seem to be using aov() with contrasts instead of the contrast tests provided by the lmerTest package for mixed models (which evidently provided your first code block) and you only have one barely significant result among your contrasts in the second code block while the mixed-model result in the first code block showed p = 0.016 for the interaction term.

This type of behavior occurs between paired and independent-groups t tests when there are substantial differences in baseline values among individuals but treatment-related differences from baseline are similar. Just like a paired t test is more powerful than an independent-groups t test in that scenario, if my guess is correct then your second code block has thrown away all the good that you did by accounting for the individual baseline differences with your mixed model. In that case you need to go back and evaluate your contrasts in a way that takes the mixed-model results into account. I understand that the lmerTest package provides such possibilities, but have little experience with that package.

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