Q105: An experiment was conducted using Randomized Block Design with 5... - Design of Experiments - Agricultural Statistics- ICAR JRF/SRF 2024 | Agrigyan

• Critical Difference (CD) and Mean Separation in RBD:
• Number of treatments ($t$) = 5; Number of replications ($r$) = 4
• Error degrees of freedom: $df_e = (t - 1)(r - 1) = (5 - 1)(4 - 1) = 12$
• Error Mean Square ($MSE$) = 18
• Tabulated critical value: $t_{0.05, 12} = 2.18$
• Standard error of difference between two treatment means ($SE_d$):

• Critical Difference (CD):

• Pairwise Treatment Comparison (Means in descending order: T1 = 65, T2 = 28, T3 = 25, T4 = 18, T5 = 9):
• $|T1 - T2| = 65 - 28 = 37 \gt 6.54$ (Significantly different)
• $|T2 - T3| = 28 - 25 = 3 \lt 6.54$ (Not significantly different $\implies$ homogeneous group (T2, T3))
• $|T3 - T4| = 25 - 18 = 7 \gt 6.54$ (Significantly different)
• $|T4 - T5| = 18 - 9 = 9 \gt 6.54$ (Significantly different)
• Homogeneous Groups: Four distinct groups: [T1, (T2, T3), T4, T5].
• Conclusion: 6.54 and four groups viz., [T1, (T2, T3), T4, T5] (Option 2).

Correct option: (2) 6.54 and four groups viz., [T1, (T2, T3), T4, T5]