A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: Total SS = 1951, SST = 349, SSE = 188. What must the value of SSB be?
A) 537
B) 1414
C) 1602
D) 1763

Question

Quizplus · Accepted Answer

The total sum of squares (SST) can be broken down into two parts: treatment sum of squares (SSB) and error sum of squares (SSE), where SST = SSB + SSE. 
We are given that SST = 349 and SSE = 188, so we can solve for SSB as follows: 
SST = SSB + SSE 
349 = SSB + 188 
SSB = 161 
However, this value of SSB assumes equal block sizes. In a randomized block design, we also need to consider variability between the blocks. We can calculate the sum of squares between the blocks (SSBlocks) using the formula: 
SSBlocks = (Total SS - SST - SSE) / (Number of Blocks - 1) 
Plugging in the given values, we get: 
SSBlocks = (1951 - 349 - 188) / (5 - 1) = 537
Therefore, the total sum of squares is made up of SSB = 161 and SSBlocks = 537, which add up to 698. The only answer choice that equals 698 when added to SSE is B) 1414.

A Randomized Block Design with 4 Treatments and 5 Blocks