R's stats::aov and nlme::lme produce conflicting results

Question

I want to use both anova and linear models to test the assumption that my some of my categories have different means than the rest.

I am using stats::aov for anova and nlme::lme for linear modelling. The full code is available in this notebook.

Basically I end up getting:

Error: ID
          Df  Sum Sq  Mean Sq F value Pr(>F)
Residuals  6 0.01198 0.001997               

Error: Within
          Df  Sum Sq  Mean Sq F value Pr(>F)  
COI        7 0.01926 0.002752    1.92 0.0903 .
Residuals 42 0.06020 0.001433 

and

Fixed effects: ER ~ COI 
                      Value  Std.Error DF   t-value p-value
(Intercept)      0.00200000 0.01465712 42 0.1364525  0.8921
COIemotion-hard  0.05600000 0.02023699 42 2.7672098  0.0084
COIscrambling-06 0.04218045 0.02023699 42 2.0843242  0.0433
COIscrambling-10 0.02094737 0.02023699 42 1.0351029  0.3065
COIscrambling-14 0.00685714 0.02023699 42 0.3388420  0.7364
COIscrambling-18 0.02085714 0.02023699 42 1.0306445  0.3086
COIscrambling-22 0.04885714 0.02023699 42 2.4142493  0.0202
COIscrambling-26 0.02742857 0.02023699 42 1.3553681  0.1825

Which means that lme is telling me 3 groups may significantly lie outside the range of the others, while aov is telling me the probability of ANY GROUP AT ALL being different from the others is not significant (using a p=0.05 cutoff).

What am I to make of this? Do I understand these results correctly?

Answer 1

The analyses being presented aren't being fairly compared so there's no way to know if they're actually saying different things. They could be perfectly compatible. You could use lm (what underlies aov) and get the treatment effects just as you have for lme. You can also find omnibus F's using lme. Then you could compare things a little better but that's not really how you decide between mixed models and repeated measures ANOVA for a particular case. Regardless, the omnibus F in an ANOVA is not about simple effects so what you're comparing is apples and pizza.

The lme and aov commands use very different kinds of analysis methods. Baayen (2008) and others have demonstrated that the mixed models used in lme are generally more powerful compared to conventional repeated measures ANOVA and they also have fewer assumptions (e.g. sphericity). That said, there is the issue that mixed models are more sensitive to normality in residuals partially because with repeated measures ANOVA you benefit from the CLT to generate normality. There are many differences and the modelling methods function differently. You should be selecting one based on theoretical grounds and not particular results. A few years ago I was pretty much told by every statistician I met that you just should never use repeated measures ANOVA. I don't think that's as universal advice as they thought it was but perhaps that will help you.

It is possible that lme is finding effects not found in your simple ANOVA using aov. It's not practically possible to get truly comparable results to decide what to believe because they are doing different things and any tests mean (slightly) different things. That said, you could at least try anova(mylmeModel) to get omnibus F tests of the mixed effects model. Then you've got something substantially more comparable than what you're presenting here.

NOTE: I also asked if CDIscrambling was a continuous variable because it's a terrible habit of those who typically use repeated measures ANOVA to turn continuous variables into multiple categories. When using mixed models don't do that. You'll get much more power out of being able to treat it as a continuous variable. If it's not linear that's a different question and you can deal with that separately.

Answer 2

(Converted from a set of comments.)

You don't have to choose because the two methods do not contradict each other in any way. One presents the omnibus test while the other tests the individual contrasts. It is a well-known fact that a non-significant omnibus test does NOT imply that none of the comparisons subsumed under that omnibus test are significant. This has nothing to do with aov() vs. lme().

The following document I found online may be useful to you:

The Meaning of the Omnibus F

wouldn't what you are saying amount to "it is normal for omnibus tests (here ANOVA) to lead to false negatives"?

Yes.

so if I run lme I would have to define a priori which conditions interest me, and simply picking the most significant ones a posteriori means I'm data mining?

Yes.