title: R- Partial eta squared for repeated measures ANOVA (car package)
body: <p>I have a 2-way repeated measures design (3 x 2), and I would like to get figures out how to calculate effect sizes (partial eta squared).</p>
  
  <p>I have a matrix with data in it (called a) like so (repeated measures)</p>
  
  <pre><code>         A.a          A.b           B.a        B.b          C.a           C.b
  1        514.0479     483.4246      541.1342   516.4149     595.5404      588.8000
  2        569.0741     550.0809      569.7574   599.1509     621.4725      656.8136
  3        738.2037     660.3058      812.2970   735.8543     767.0683      738.7920
  4        627.1101     638.1338      641.2478   682.7028     694.3569      761.6241
  5        599.3417     637.2846      599.4951   632.5684     626.4102      677.2634
  6        655.1394     600.9598      729.3096   669.4189     728.8995      716.4605
  </code></pre>
  
  <p>idata = </p>
  
  <pre><code>    Caps    Lower
         A       a
         A       b
         B       a
         B       b
         C       a
         C       b
  </code></pre>
  
  <p>I know how to do a repeated measures ANOVA with the car package (type 3 SS is standard in my field although I know that it results in a logical error.. if somebody wants to explain that to me like I'm 5 I would love to understand it):</p>
  
  <pre><code>summary(Anova(lm(a ~ 1),
            idata=idata,type=3, 
            idesign=~Caps*Lower)),
      multivariate=FALSE)
  </code></pre>
  
  <p>I think what I want to do is take this part of the summary print out: </p>
  
  <p>Univariate Type III Repeated-Measures ANOVA Assuming Sphericity</p>
  
  <pre><code>                     SS num Df Error SS den Df        F    Pr(&gt;F)    
  (Intercept)     14920141     1   153687      5 485.4072 3.577e-06 ***
  Caps            33782        2     8770     10  19.2589  0.000372 ***
  Lower           195          1    13887      5   0.0703  0.801451    
  Caps:Lower      2481         2      907     10  13.6740  0.001376 ** 
  </code></pre>
  
  <p>And use it to calculate partial ETA squared. So, if I'm not mistaken, I need to take the SS from the first column and divide it by (itself + SS Error for that row) for each effect. Is this the correct way to go about it? If so, how do I do it? I can't figure out how to reference values from the summary print out.</p>