Complete the following table for the analysis of variance of design.

S.V. d.f S.S MSS F
Blocks 3 45.5 ? ?
Treatments 4 ? ? ?
Error ? ? 3.6 ?
Total ? 120.89

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Solution:

The given is of Randomized Block Design(RBD).

Numbers of blocks = r – 1 = 3 ⇒ r = 4

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

Error (for d.f) = (r-1)(t-1) = (4-1)(5-1) = 12

Total(for d.f) = rt – 1 = 4.5 – 1 = 19         Note: You can also add DF for blocks, DF for treatment and error to get total DF.

Now,

MSB = \(\frac{SSB}{D.F.}\) = \(\frac{45.5}{3}\) = 15.17

 

MSB = \(\frac{SSE}{D.F.}\)

3.6 = \(\frac{SSE}{12.}\)

SSE = 43.2

 

SST = TSS – SSB – SSE

= 120.89 – 45.5 – 43.2

= 32.19

 

MST = \(\frac{SST}{D.F.}\) = \(\frac{32.19}{4}\) = 8.0475

 

Fb = \(\frac{MSB}{SSB}\) = \(\frac{15.7}{45.5}\) = 0.35

Ft = \(\frac{MST}{SST}\) = \(\frac{8.0475}{32.19}\) = 0.25

Fe = \(\frac{MSE}{SSE}\) = \(\frac{3.6}{43.2}\) = 0.083

Hence, the table after filling missing value is

S.V. d.f S.S MSS F
Blocks 3 45.5 15.17 0.35
Treatments 4 32.19 8.0475 0.25
Error 12 43.2 3.6 0.083
Total 19 120.89
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