title: How do I interpret the TukeyHSD output in R? (in relation to the underlying regression model)
body: <p>I built a simple linear regression model with 'Score' as the dependent variable, and 'Activity' as the independent one. 'Activity' has 5 levels: 'listen' (reference level), 'read1', 'read2', 'watch1', 'watch2'. </p>
  
  <pre><code>Call:
  lm(formula = Score ~ Activity)
  
  Residuals:
       Min       1Q   Median       3Q      Max 
  -22.6154  -8.6154  -0.6154   7.1346  31.3846 
  
  Coefficients:
                 Estimate Std. Error t value Pr(&gt;|t|)    
  (Intercept)      41.615      2.553  16.302   &lt;2e-16 ***
  Activityread1     6.385      7.937   0.804   0.4254    
  Activityread2    20.885      9.552   2.186   0.0340 *  
  Activitywatch1    3.885      4.315   0.900   0.3728    
  Activitywatch2  -11.415      6.357  -1.796   0.0792 .  
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  
  Residual standard error: 13.02 on 45 degrees of freedom
  Multiple R-squared:  0.1901,    Adjusted R-squared:  0.1181 
  F-statistic:  2.64 on 4 and 45 DF,  p-value: 0.04594
  </code></pre>
  
  
  
  <p>In order to obtain all pairwise comparisons, I performed a TukeyHSD test, whose output I'm having difficulty interpreting. While the output of the model shows that the only significant effect we have is due to the contrast between 'listen' and 'read2', the TukeyHSD results yield that the only significant contrast exists between 'watch2' and 'read2'. What does this mean?</p>
  
  <p><div class="snippet" data-lang="js" data-hide="false" data-console="true" data-babel="false">
  <div class="snippet-code">
  <pre class="snippet-code-js lang-js prettyprint-override"><code>&gt; TukeyHSD(aov(mod4), "Activity")
    Tukey multiple comparisons of means
      95% family-wise confidence level
  
  Fit: aov(formula = mod4)
  
  $Activity
                      diff        lwr       upr     p adj
  read1-listen    6.384615 -16.168371 28.937602 0.9279144
  read2-listen   20.884615  -6.256626 48.025857 0.2034549
  watch1-listen   3.884615  -8.376548 16.145779 0.8952957
  watch2-listen -11.415385 -29.477206  6.646437 0.3885969
  read2-read1    14.500000 -19.264610 48.264610 0.7397464
  watch1-read1   -2.500000 -26.031639 21.031639 0.9981234
  watch2-read1  -17.800000 -44.811688  9.211688 0.3466391
  watch1-read2  -17.000000 -44.959754 10.959754 0.4278714
  watch2-read2  -32.300000 -63.245777 -1.354223 0.0368820
  watch2-watch1 -15.300000 -34.569930  3.969930 0.1783961</code></pre>
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