title: How does emmeans calculate confidence intervals used to compare means
body: <p>I'm looking for more background and documentation on how <code>emmeans</code> calculates confidence intervals used in the graphical comparison of means outlined in the following vignette:
  <a href="https://cran.r-project.org/web/packages/emmeans/vignettes/comparisons.html#graphical" rel="nofollow noreferrer">https://cran.r-project.org/web/packages/emmeans/vignettes/comparisons.html#graphical</a></p>
  
  <p>In the "Graphical Comparisons" section there is an example of what I am referring to. In particular, I am interested in the red lines with arrows used for comparing means.</p>
  
  <p>It reads: </p>
  
  <blockquote>
    <p>If an arrow from one mean overlaps an arrow from another group, the difference is not “significant”.</p>
  </blockquote>
  
  <p>But how are the red line intervals used for comparing means calculated? Is this documented somewhere?</p>