# 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

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
There may be error in calculation. Please follow the steps only. If you find any error then please report to us.