Followup tests

The text below continues on from this example of factorial Anova.

If we want to look at post-hoc pairwise tests we can use the the emmeans() function from the emmeans:: package. By default Tukey correction is applied for multiple comparisons, which is a reasonable default:

em <- emmeans::emmeans(eysenck.model, pairwise~Age:Condition)
em$contrasts
 contrast                          estimate   SE df t.ratio p.value
 Young,Counting - Older,Counting        0.5 1.27 90   0.395 1.0000 
 Young,Counting - Young,Rhyming         0.1 1.27 90   0.079 1.0000 
 Young,Counting - Older,Rhyming        -0.6 1.27 90  -0.474 1.0000 
 Young,Counting - Young,Adjective      -4.0 1.27 90  -3.157 0.0633 
 Young,Counting - Older,Adjective      -7.8 1.27 90  -6.157 <.0001 
 Young,Counting - Young,Imagery        -6.4 1.27 90  -5.052 0.0001 
 Young,Counting - Older,Imagery       -10.6 1.27 90  -8.367 <.0001 
 Young,Counting - Young,Intention      -5.0 1.27 90  -3.947 0.0058 
 Young,Counting - Older,Intention     -12.3 1.27 90  -9.709 <.0001 
 Older,Counting - Young,Rhyming        -0.4 1.27 90  -0.316 1.0000 
 Older,Counting - Older,Rhyming        -1.1 1.27 90  -0.868 0.9970 
 Older,Counting - Young,Adjective      -4.5 1.27 90  -3.552 0.0205 
 Older,Counting - Older,Adjective      -8.3 1.27 90  -6.551 <.0001 
 Older,Counting - Young,Imagery        -6.9 1.27 90  -5.446 <.0001 
 Older,Counting - Older,Imagery       -11.1 1.27 90  -8.761 <.0001 
 Older,Counting - Young,Intention      -5.5 1.27 90  -4.341 0.0015 
 Older,Counting - Older,Intention     -12.8 1.27 90 -10.103 <.0001 
 Young,Rhyming - Older,Rhyming         -0.7 1.27 90  -0.553 0.9999 
 Young,Rhyming - Young,Adjective       -4.1 1.27 90  -3.236 0.0511 
 Young,Rhyming - Older,Adjective       -7.9 1.27 90  -6.236 <.0001 
 Young,Rhyming - Young,Imagery         -6.5 1.27 90  -5.131 0.0001 
 Young,Rhyming - Older,Imagery        -10.7 1.27 90  -8.446 <.0001 
 Young,Rhyming - Young,Intention       -5.1 1.27 90  -4.025 0.0044 
 Young,Rhyming - Older,Intention      -12.4 1.27 90  -9.787 <.0001 
 Older,Rhyming - Young,Adjective       -3.4 1.27 90  -2.684 0.1963 
 Older,Rhyming - Older,Adjective       -7.2 1.27 90  -5.683 <.0001 
 Older,Rhyming - Young,Imagery         -5.8 1.27 90  -4.578 0.0006 
 Older,Rhyming - Older,Imagery        -10.0 1.27 90  -7.893 <.0001 
 Older,Rhyming - Young,Intention       -4.4 1.27 90  -3.473 0.0260 
 Older,Rhyming - Older,Intention      -11.7 1.27 90  -9.235 <.0001 
 Young,Adjective - Older,Adjective     -3.8 1.27 90  -2.999 0.0950 
 Young,Adjective - Young,Imagery       -2.4 1.27 90  -1.894 0.6728 
 Young,Adjective - Older,Imagery       -6.6 1.27 90  -5.209 0.0001 
 Young,Adjective - Young,Intention     -1.0 1.27 90  -0.789 0.9986 
 Young,Adjective - Older,Intention     -8.3 1.27 90  -6.551 <.0001 
 Older,Adjective - Young,Imagery        1.4 1.27 90   1.105 0.9830 
 Older,Adjective - Older,Imagery       -2.8 1.27 90  -2.210 0.4578 
 Older,Adjective - Young,Intention      2.8 1.27 90   2.210 0.4578 
 Older,Adjective - Older,Intention     -4.5 1.27 90  -3.552 0.0205 
 Young,Imagery - Older,Imagery         -4.2 1.27 90  -3.315 0.0411 
 Young,Imagery - Young,Intention        1.4 1.27 90   1.105 0.9830 
 Young,Imagery - Older,Intention       -5.9 1.27 90  -4.657 0.0005 
 Older,Imagery - Young,Intention        5.6 1.27 90   4.420 0.0011 
 Older,Imagery - Older,Intention       -1.7 1.27 90  -1.342 0.9409 
 Young,Intention - Older,Intention     -7.3 1.27 90  -5.762 <.0001 

P value adjustment: tukey method for comparing a family of 10 estimates 

Both cell means and pairwise contrasts are shown here. There is much more detail on computing pairwise comparisons and other types of contrasts in the section on multiple comparisons, including ways to extract and present your comparisons in APA format.