S.V. | d.f | S.S | MSS | F |

Blocks | 3 | 45.5 | ? | ? |

Treatments | 4 | ? | ? | ? |

Error | ? | ? | 3.6 | ? |

Total | ? | 120.89 |

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Login Now**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

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

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

F_{e} = \(\frac{MSE}{SSE}\) = \(\frac{3.6}{43.2}\) = 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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