title: Degrees of freedom ezANOVA after sphericity correction
body: <p>I've set up an ANOVA with the function <code>ezANOVA</code> from the package <code>ez</code>. There are sphericity corrections and I see different p-values because of the different degrees of freedom. 
  But how can I see the new degrees of freedom?</p>
  
  <p>This is an output from a predefined ANOVA:</p>
  
  <pre><code>$ANOVA
             Effect DFn DFd           F            p p&lt;.05        ges
  2           group   1  18   18.430592 4.377562e-04     * 0.07633358
  3             cue   3  54  516.605213 1.005518e-39     * 0.89662286
  5           flank   2  36 1350.598810 1.386546e-34     * 0.92710583
  4       group:cue   3  54    2.553236 6.497492e-02       0.04110445
  6     group:flank   2  36    8.768499 7.900829e-04     * 0.07627434
  7       cue:flank   6 108    5.193357 9.938494e-05     * 0.11436699
  8 group:cue:flank   6 108    6.377225 9.012515e-06     * 0.13686958
  
  $`Mauchly's Test for Sphericity`
             Effect         W         p p&lt;.05
  3             cue 0.7828347 0.5366835      
  4       group:cue 0.7828347 0.5366835      
  5           flank 0.8812738 0.3415406      
  6     group:flank 0.8812738 0.3415406      
  7       cue:flank 0.1737053 0.1254796      
  8 group:cue:flank 0.1737053 0.1254796      
  
  $`Sphericity Corrections`
             Effect       GGe        p[GG] p[GG]&lt;.05       HFe        p[HF] p[HF]&lt;.05
  3             cue 0.8652559 1.115029e-34         * 1.0239520 1.005518e-39         *
  4       group:cue 0.8652559 7.472046e-02           1.0239520 6.497492e-02          
  5           flank 0.8938738 3.763312e-31         * 0.9858964 3.964046e-34         *
  6     group:flank 0.8938738 1.297752e-03         * 0.9858964 8.438369e-04         *
  7       cue:flank 0.6022111 1.546166e-03         * 0.7721473 4.745714e-04         *
  8 group:cue:flank 0.6022111 3.424499e-04         * 0.7721473 7.170939e-05         *
  </code></pre>
  
  <p>With Greenhouse-Geisser are the new degrees of freedom for <code>cue</code> simply 0.8652559 times the original dfs 3 and 54 or is it more difficult?</p>