Differents results depending order of independent variables in ANOVA

[Rodrigo Badilla]

Hi all,

I am having differents results in a Anova analysis depending order of independent variables, to replicate this I use Casella (2008) datasets and sequential Sum of squares:

clear all
set more off
input Diet    Tank    WtGain
1    1    9.759
1    1    7.399
1    1    -0.209
1    1    2.204
1    1    0.267
1    1    3.002
1    2    8.031
1    2    6.25
1    2    0.134
1    2    4.594
1    2    4.414
1    2    9.816
1    3    -2.23
1    3    9.69
1    3    -2.239
1    3    9.499
1    3    6.927
1    3    3.449
1    4    4.274
1    4    7.52
1    4    12.141
1    4    4.828
1    4    3.391
1    4    3.621
2    5    21.819
2    5    6.503
2    5    31.596
2    5    24.633
2    5    15.73
2    5    22.231
2    6    11.672
2    6    26.479
2    6    19.784
2    6    20.884
2    6    21.811
2    6    26.344
2    7    22.161
2    7    16.429
2    7    23.311
2    7    21.983
2    7    12.181
2    7    18.252
2    8    30.865
2    8    17.875
2    8    24.562
2    8    20.442
2    8    20.791
2    8    19.44
3    9    47.588
3    9    38.219
3    9    44.445
3    9    47.115
3    9    30.83
3    9    58.708
3    10    62.477
3    10    29.834
3    10    49.902
3    10    59.946
3    10    46.587
3    10    38.567
3    11    54.545
3    11    38.846
3    11    52.163
3    11    43.141
3    11    27.822
3    11    58.025
3    12    57.749
3    12    47.737
3    12    40.653
3    12    45.344
3    12    46.702
3    12    50.091
end

. anova WtGain Diet Tank, sequential

                           Number of obs =      72     R-squared     =  0.8738
                           Root MSE      = 7.17084     Adj R-squared =  0.8506

                  Source |    Seq. SS     df       MS           F     Prob > F
              -----------+----------------------------------------------------
                   Model |  21355.5538    11  1941.41398      37.76     0.0000
                         |
                    Diet |  21247.7397     2  10623.8699     206.61     0.0000
                    Tank |  107.814082     9  11.9793424       0.23     0.9883
                         |
                Residual |  3085.25287    60  51.4208811  
              -----------+----------------------------------------------------
                   Total |  24440.8067    71  344.236714  

. anova WtGain Tank Diet , sequential

                           Number of obs =      72     R-squared     =  0.8738
                           Root MSE      = 7.17084     Adj R-squared =  0.8506

                  Source |    Seq. SS     df       MS           F     Prob > F
              -----------+----------------------------------------------------
                   Model |  21355.5538    11  1941.41398      37.76     0.0000
                         |
                    Tank |  21355.5538    11  1941.41398      37.76     0.0000
                    Diet |           0     0
                         |
                Residual |  3085.25287    60  51.4208811  
              -----------+----------------------------------------------------
                   Total |  24440.8067    71  344.236714

Do you know why?

Thanks in advance
Regards
Rodrigo

[William Lisowski]

Since Diet is constant within each value of Tank, once Tank is used, Diet provides no additional information.

[Carlo Lazzaro]

Rodrigo:
what you experienced is explained, also in graphical terms, in https://www.stata.com/bookstore/hand...nalyses-stata/, pages 104-108.

[Rodrigo Badilla]

Thanks William and Carlo for you reply. I appreciate it.
Regards
Rodrigo