Partitioning the Sums of Squares (5 of 7)
For the example,
SSE1 = (3-4)² + (5-4)² +( 3-4)² + (5-4)² = 4
SSE2 = (2-3)² + (4-3)² + (2-3)² + (4-3)² = 4
SSE3 = (2-2)² + (1-2)² + (3-2)² + (2-2)² = 2
Therefore,
SSE = SSE1 + SSE2 + SSE3 = 4 + 4 + 2 = 10.
They All Add Up
The sums of squares computed in this example are:
SST = 18
SSB = 8
SSE = 10.
Notice that SST = SSB + SSE. This is important because it shows that the total sum of squares can be divided into two components: the sum of squares due to treatments (SSB) and the sum of squares that not due to treatments (SSE).