how to interpret manova(rm) results

Question

Kate Feller on 22 Apr 2021

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https://se.mathworks.com/matlabcentral/answers/810140-how-to-interpret-manova-rm-results

Commented: Scott MacKenzie on 4 Aug 2021

Hello,

I collected measurements of 15 separate animals at 5 time points (T1-T5). I would like to test for significant variation among individuals at each time point, but also across time points for each animal using a MANOVA with repeated measures. While formatting the data and running the code was quite straightforward, I'm struggling to find a good explanation of the output tables and how to interpret them.

Many thanks for the help.

Here is my code and the subsequent output tables I speak of:

   rm = fitrm(my_table, 'T1-T5~animal');
    manova(rm)
    
ans =
  8×9 table
     Within       Between      Statistic     Value       F       RSquare    df1    df2     pValue 
    ________    ___________    _________    _______    ______    _______    ___    ___    ________
    Constant    (Intercept)    Pillai       0.58133    3.1242    0.58133     4      9     0.071884
    Constant    (Intercept)    Wilks        0.41867    3.1242    0.58133     4      9     0.071884
    Constant    (Intercept)    Hotelling     1.3885    3.1242    0.58133     4      9     0.071884
    Constant    (Intercept)    Roy           1.3885    3.1242    0.58133     4      9     0.071884
    Constant    podnum         Pillai       0.44393    1.7963    0.44393     4      9      0.21373
    Constant    podnum         Wilks        0.55607    1.7963    0.44393     4      9      0.21373
    Constant    podnum         Hotelling    0.79834    1.7963    0.44393     4      9      0.21373
    Constant    podnum         Roy          0.79834    1.7963    0.44393     4      9      0.21373
    
    
    manova(rm,'By', ('animal')
    
ans =
  56×9 table
     Within      Between     Statistic     Value        F       RSquare    df1    df2     pValue 
    ________    _________    _________    _______    _______    _______    ___    ___    ________
    Constant    animal=1     Pillai       0.59093     3.2503    0.59093     4      9     0.065534
    Constant    animal=1     Wilks        0.40907     3.2503    0.59093     4      9     0.065534
    Constant    animal=1     Hotelling     1.4446     3.2503    0.59093     4      9     0.065534
    Constant    animal=1     Roy           1.4446     3.2503    0.59093     4      9     0.065534
    Constant    animal=2     Pillai       0.60085      3.387    0.60085     4      9     0.059394
    Constant    animal=2     Wilks        0.39915      3.387    0.60085     4      9     0.059394
    ...
    Constant    animal=14    Hotelling    0.43544    0.97973    0.30335     4      9      0.46496
    Constant    animal=14    Roy          0.43544    0.97973    0.30335     4      9      0.46496
    Constant    animal=15    Pillai       0.30201    0.97354    0.30201     4      9       0.4678
    Constant    animal=15    Wilks        0.69799    0.97354    0.30201     4      9       0.4678
    Constant    animal=15    Hotelling    0.43268    0.97354    0.30201     4      9       0.4678
    Constant    animal=15    Roy          0.43268    0.97354    0.30201     4      9       0.4678