Yields are noted for tree samples from four different varieties in crops in Argentina.
The following varieties are: Variety A = 15, 14, 12, 13
Variety B = 11, 18, 13
Variety C = 18, 25, 19, 20
Variety D = 19, 20, 24.
My "teacher" gave me the values of:
SS Variety = 172.36 SS Error = 74
I am competent with calculating degrees of freedom. But here, he provided me with these values, I would like to ask how they calculated.
My knowledge with ANOVA is that SS = Sum of Squares. With other examples I would square each data value - but I would think that it would clearly exceed the value given.
And so I am asking - how this value is calculated.
Thanks.
The overall mean is about $17.21429$ while the means for each variety are $13.5,14,20.5,21$
What you are describing as SS Variety is calculated as $$4\times (13.5-17.21429)^2 + 3\times (14-17.21429)^2 + 4\times (20.5-17.21429)^2 + 3\times (21.5-17.21429)^2$$
What you are describing as SS Error is calculated as $$(15-13.5)^2 + (14-13.5)^2 + (12-13.5)^2 + (13-13.5)^2 + \\ (11-14)^2 + (13-14)^2 + (18-14)^2 + \\ (18-20.5)^2 + (25-20.5)^2 + (19-20.5)^2 + (20-20.5)^2 + \\ (19-21)^2 + (20-21)^2 + (24-21)^2 $$
If you add these together, you get the overall sum of squares of differences from the overall mean of about $246.3571$