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Forgive me for this, but I just can't work it out.

Some dummy data :

r1 <- rnorm(40)
r2 <- rnorm(40)
r2 <- r2[order(r2)]
f1 <- as.factor(c(rep(0, 20), rep(1, 20)))
g1 <- as.factor(c(rep("A", 40), rep("B", 40)))
dat <- data.frame(r = c(r1, r2), f = c(f1,f1), g = g1)

Then the model:

contrasts(dat$f) <- cbind(c(-1,1))
contrasts(dat$g) <- cbind(c(-1,1))
m <- aov(r ~ f*g, data = dat)

summary(m)
             Df Sum Sq Mean Sq F value   Pr(>F)    
 f            1   6.54   6.536   9.056  0.00355 ** 
 g            1   0.00   0.004   0.005  0.94211    
 f:g          1  14.06  14.056  19.476 3.32e-05 ***
 Residuals   76  54.85   0.722                   

Then with emmeans:

 emmeans(m, pairwise ~ f | g)

 $emmeans
 g = A:
 f  emmean   SE df lower.CL upper.CL
 0 -0.0646 0.19 76   -0.443   0.3138
 1 -0.3313 0.19 76   -0.710   0.0471

 g = B:
 f  emmean   SE df lower.CL upper.CL
 0 -0.8891 0.19 76   -1.267  -0.5107
 1  0.5209 0.19 76    0.143   0.8992

 Confidence level used: 0.95 

 $contrasts
 g = A:
 contrast estimate    SE df t.ratio p.value
 0 - 1       0.267 0.269 76  0.993  0.3240 

 g = B:
 contrast estimate    SE df t.ratio p.value
 0 - 1      -1.410 0.269 76 -5.248  <.0001 

My regrettably naive question is, what test is applied to generate the contrast read out here? Or more broadly, is this information made available in the emmeans output somewhere?

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1 Answer 1

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The EMMs shown are the predictions from the model for each of the 4 possible combinations of the levels of the two factors. The contrasts shown are differences of those estimates. Those differences are divided by their SEs to form the t ratios, which in turn are used to compute two-sided p values using tail areas of the t distribution with the given df.

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