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An experiment was conducted using Randomized Block Design with 5 treatments and 4 replications and the ANOVA table is given below:
Let the treatment means be T1 = 65, T2 = 28, T3 = 25, T4 = 18, and T5 = 9. Given tabulated $t_{0.05}$ at 12 df is 2.18, find the Critical Difference (CD) and significantly different treatment groups:
| Source | Sum of Squares | Mean Sum of Squares |
|---|---|---|
| Blocks | 60 | 20 |
| Treatments | 1000 | 250 |
| Error | 216 | 18 |
| Total | 1276 |
EXPLANATION
Linear Estimation, Gauss-Markov Theorem & Bas
- 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]
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