Eta²ANOVA重复测量

Question

我做了一个重复测量的方差分析：

> Type III Repeated Measures MANOVA Tests:

> Term: (Intercept) Response transformation matrix:
 (Intercept)
> [1,]           1
> [2,]           1
> [3,]           1
> [4,]           1

> Sum of squares and products for the hypothesis:
        (Intercept)
> (Intercept)    381.3062

> Sum of squares and products for error:
        (Intercept)
> (Intercept)    3.346528

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


> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> Term: storytype Response transformation matrix:
 storytype1
> [1,]         -1
> [2,]         -1
> [3,]          1
> [4,]          1

> Sum of squares and products for the hypothesis:
       storytype1
> storytype1    0.75625

> Sum of squares and products for error:
       storytype1
> storytype1   2.479861

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

> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> Term: questiontype 
> Response transformation matrix:
 questiontype1
> [1,]            -1
> [2,]             1
> [3,]            -1
> [4,]             1

> Sum of squares and products for the hypothesis:
          questiontype1
> questiontype1     0.4340278

> Sum of squares and products for error:
          questiontype1
 > questiontype1      1.496528

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

> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> Term: storytype:questiontype 

>  Response transformation matrix:
 storytype1:questiontype1
> [1,]                        1
> [2,]                       -1
> [3,]                       -1
> [4,]                        1

> Sum of squares and products for the hypothesis:
                     storytype1:questiontype1
> storytype1:questiontype1               0.01736111

> Sum of squares and products for error:
                     storytype1:questiontype1
> storytype1:questiontype1                 1.385417

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

> Univariate Type III Repeated-Measures ANOVA Assuming Sphericity

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

现在我想测试效果大小，我在这里找到了解决方案，所以我做到了：

> #install.packages("heplots")
> library(heplots)
> etasq(anovaModel, anova=TRUE) #0.9919

R回答：

> Note: model has only an intercept; equivalent type-III tests substituted.
            eta^2
> (Intercept) 0.9918861

有人可以向我解释这是对的吗？不是0.99极高吗？