I have run a linear mixed-effects model using lmer package. I'm using year sampled (1990s or 2017), field(1967 or 1984), and treatment (open or closed) to determine differences in native herbaceous percent cover. I am using this model since I have two data points (year.sampled: 90s and 2017).

Model code:

model2<-lmer(Native.Herbaceous.Percent.Cover~TreatmentYear.SampledField+(1|HerbPC$Plot),data = HerbPC)

I have set my plot names as my random effect.

The model runs successfully and a run an anova on the model. anova(model2) and I receive this anova result

As you can see the interaction between the variables treatment and year sampled (Treatment:Year.Sampled) is not significant at 0.566.

When I run a post hoc tukey on this interaction using emmeans(object=model2, pairwise~Treatment*Year.Sampled, adjust="tukey") I receive this tukey result

As you can see this emmeans tukey is showing 4 different significant pairwise interactions.

I am wondering why my anova of the model shows no significance of treatment and year sampled while my tukey shows multiple significant pairwise interactions of these variables?

I see that the emmeans tukey results are averaged over the levels "Fields" variable. Is the difference because the anova of treatment:year.sampled interactions is independent of fields, while the emmeans tukey is not?

Thanks for the help.


This isn’t just the interaction! The comparisons you did involve the effects of Treatment, Year.Sampled, and their interaction. Note for example that the average of the first and last contrasts is the marginal comparison of Treatment, averaged over the two years. Similarly, the average of the 2nd and 5th contrasts is the marginal Year.Sampled difference, averaged over treatments.

  • $\begingroup$ I see what you are saying and I do understand that this tukey will test interactions of year.sampled and treatment as well as the the marginal difference of each one independently. I'm wondering why I would see such a high F value in the omnibus ANOVA but several strongly significant p values in the multiple comparisons tukey? Can you shed some light on this @rvl? $\endgroup$
    – btp7rr
    Mar 5 '19 at 17:33
  • 2
    $\begingroup$ I think you're looking too hard at asterisks and P values. Look at the results graphically, say via emmip(model2, Treatment ~ Year.Sampled). Relate each of the comparisons listed in the $contrasts table to which pair of points are being compared in the graph, and it will better help you understand what the comparisons are --- and the fact that those comparisons include main effects, not just the interaction effects. $\endgroup$
    – Russ Lenth
    Mar 5 '19 at 23:07

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