title: calculate variance in effect coding
body: <p>I want to calculate standard error or more accuratly a Confidence-interval for
  an effect coded variable. Here's a minimal example:</p>
  
  <pre><code>data(mtcars)
  mtcars$gearEff &lt;- C(factor(mtcars$gear), sum, 3)
  contrasts(mtcars$gearEff)
    [,1] [,2]
  3    1    0
  4    0    1
  5   -1   -1
  mod1 &lt;- lm(mpg ~ gearEff, data=mtcars)
  summary(mod1)
  
  ##..truncated output...
  Coefficients:
              Estimate Std. Error t value Pr(&gt;|t|)    
  (Intercept)  20.6733     0.9284  22.267  &lt; 2e-16 ***
  gearEff1     -4.5667     1.1639  -3.924 0.000492 ***
  gearEff2      3.8600     1.2156   3.175 0.003534 ** 
  ###...
  </code></pre>
  
  <p>I now am able to calculate the gearEff3 effect via:</p>
  
  <pre><code>-coef(mod1)["gearEff1"] - coef(mod1)["gearEff2"]
  0.7066667 
  </code></pre>
  
  <p>Does anyone know how to compute a confidence interval or the standard deviation
  for the gearEff3? My final goal is to plot a Foresplot with these data, but I am 
  not able to calculate this confidence interval. Help would be greatly appreciated.</p>