A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total)= 1,951,SST = 349,SSE = 188 .The value of SSB must be:
A)537
B)1,763
C)1,414
D)1,602

Question

Quizplus · Accepted Answer

Using the formula for sum of squares due to blocks:

SSB = SST - SSE - SSError

Substituting the given values:

SSB = 349 - 188 - SSError

We need to find the value of SSError.

Using the formula for sum of squares error:

SSE = (n-1) * MSerror

Where n is the total number of observations and MSerror is the mean sum of squares error.

Substituting the given values:

188 = (4*5 - 1) * MSerror

MSerror = 188 / 19 = 9.89

Substituting this value back into the equation for SSB:

SSB = 349 - 188 - (4*9.89) = 1,414

Therefore, the answer is C.

A Randomized Block Design with 4 Treatments and 5 Blocks