# how to interpret manova(rm) results

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Kate Feller on 22 Apr 2021
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
Scott MacKenzie on 4 Aug 2021
It might help if you post the data.

Manas Meena on 2 Jun 2021