Eta² ANOVA repeated measure
<p>I've done an ANOVA with repeated measure:</p>

<pre><code>&gt; Type III Repeated Measures MANOVA Tests:

&gt; Term: (Intercept) Response transformation matrix:
 (Intercept)
&gt; [1,]           1
&gt; [2,]           1
&gt; [3,]           1
&gt; [4,]           1

&gt; Sum of squares and products for the hypothesis:
        (Intercept)
&gt; (Intercept)    381.3062

&gt; Sum of squares and products for error:
        (Intercept)
&gt; (Intercept)    3.346528

&gt; Multivariate Tests: (Intercept)
            &gt; Df test stat approx F num Df den Df     Pr(&gt;F)    
&gt; Pillai            1    0.9913 4443.694      1     39 &lt; 2.22e-16 ***
&gt; Wilks             1    0.0087 4443.694      1     39 &lt; 2.22e-16 ***
&gt; Hotelling-Lawley  1  113.9409 4443.694      1     39 &lt; 2.22e-16 ***
&gt; Roy               1  113.9409 4443.694      1     39 &lt; 2.22e-16 ***


&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

&gt; Term: storytype Response transformation matrix:
 storytype1
&gt; [1,]         -1
&gt; [2,]         -1
&gt; [3,]          1
&gt; [4,]          1

&gt; Sum of squares and products for the hypothesis:
       storytype1
&gt; storytype1    0.75625

&gt; Sum of squares and products for error:
       storytype1
&gt; storytype1   2.479861

&gt; Multivariate Tests: storytype
             Df test stat approx F num Df den Df    Pr(&gt;F)   
&gt; Pillai            1 0.2336910 11.89331      1     39 0.0013658 **
&gt; Wilks             1 0.7663090 11.89331      1     39 0.0013658 **
&gt; Hotelling-Lawley  1 0.3049566 11.89331      1     39 0.0013658 **
&gt; Roy               1 0.3049566 11.89331      1     39 0.0013658 **

&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

&gt; Term: questiontype 
&gt; Response transformation matrix:
 questiontype1
&gt; [1,]            -1
&gt; [2,]             1
&gt; [3,]            -1
&gt; [4,]             1

&gt; Sum of squares and products for the hypothesis:
          questiontype1
&gt; questiontype1     0.4340278

&gt; Sum of squares and products for error:
          questiontype1
 &gt; questiontype1      1.496528

&gt; Multivariate Tests: questiontype
             Df test stat approx F num Df den Df    Pr(&gt;F)   
&gt; Pillai            1 0.2248201  11.3109      1     39 0.0017376 **
&gt; Wilks             1 0.7751799  11.3109      1     39 0.0017376 **
&gt; Hotelling-Lawley  1 0.2900232  11.3109      1     39 0.0017376 **
&gt; Roy               1 0.2900232  11.3109      1     39 0.0017376 **

&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

&gt; Term: storytype:questiontype 

&gt;  Response transformation matrix:
 storytype1:questiontype1
&gt; [1,]                        1
&gt; [2,]                       -1
&gt; [3,]                       -1
&gt; [4,]                        1

&gt; Sum of squares and products for the hypothesis:
                     storytype1:questiontype1
&gt; storytype1:questiontype1               0.01736111

&gt; Sum of squares and products for error:
                     storytype1:questiontype1
&gt; storytype1:questiontype1                 1.385417

&gt; Multivariate Tests: storytype:questiontype
             Df test stat  approx F num Df den Df  Pr(&gt;F)
&gt; Pillai            1 0.0123762 0.4887218      1     39 0.48865
&gt; Wilks             1 0.9876238 0.4887218      1     39 0.48865
&gt; Hotelling-Lawley  1 0.0125313 0.4887218      1     39 0.48865
&gt; Roy               1 0.0125313 0.4887218      1     39 0.48865

&gt; Univariate Type III Repeated-Measures ANOVA Assuming Sphericity

                       SS num Df Error SS den Df         F    Pr(&gt;F)    
&gt; (Intercept)            95.327      1  0.83663     39 4443.6935 &lt; 2.2e-16 ***
&gt; storytype               0.189      1  0.61997     39   11.8933  0.001366 ** 
&gt; questiontype            0.109      1  0.37413     39   11.3109  0.001738 ** 
&gt; storytype:questiontype  0.004      1  0.34635     39    0.4887  0.488647    
</code></pre>

<p>Now I wanted to test the Effect size and I've found a solution here, so I have done this:</p>

<pre><code>&gt; #install.packages("heplots")
&gt; library(heplots)
&gt; etasq(anovaModel, anova=TRUE) #0.9919
</code></pre>

<p>R answered: </p>

<pre><code>&gt; Note: model has only an intercept; equivalent type-III tests substituted.
            eta^2
&gt; (Intercept) 0.9918861
</code></pre>

<p>Can anyone explain to me if this was right? Isn't 0.99 extremly high? </p>