Complete the following table

SV Df SS MSS F
Blocks 5 27 ? ?
Treatment 4 ? ? ?
Error ? ? 4
Total ? 88

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Solution:

The given is of Randomized Block Design(RBD).

Numbers of blocks = r – 1 = 5 ⇒ r = 6

Numbers of treatment = t – 1 = 4 ⇒ t = 5

Error (for d.f) = (r-1)(t-1) = (6-1)(5-1) = 20

Total(for d.f) = rt – 1 = 6.5 – 1 = 29         Note: You can also add DF for blocks, DF for treatment and error to get total DF.

Now,

MSB = \(\frac{SSB}{df} = \frac{27}{5}\) = 5.4

 

\(MSE = \frac{SSE}{df}\)

\(4= \frac{SSE}{20}\)

SSE = 80

 

SST = TSS – SSE – SSB

SST = 88 – 80 -29

SST = -19

 

MST = \(\frac{SST}{df} = \frac{-19}{4}\) = -4.75

 

Fblock = \(\frac{MSB}{SST} = \frac{5.4}{27}\) = 0.2

Ftreatment = \(\frac{MSB}{SST} = \frac{5.4}{27}\) = 0.25

Hence, the table after filling missing value is

S.V. d.f S.S MSS F
Blocks 5 27 5.4 0.2
Treatments 4 -19 -4.75 0.25
Error 20 80 4
Total 29 88
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