Question

In a field experiment conducted under RBD, the number of replications and the treatments should be adjusted in such a way that the error degree of freedom (d.f.) becomes :
(A) $<$ 12
(B) At least 12
(C) 12 or more
(D) n-12

• A. (A), (B) and (D) only.
• B. (B) and (C) only.
• C. (C) and (D).
• D. (B), (C) and (D) only.

Hint:

If you have a small number of treatments, you must increase the number of replications ($r$) to ensure the error degrees of freedom, calculated as $(r-1)(t-1)$, is at least 12.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In agricultural field experiments designed using a Randomized Block Design (RBD), controlling experimental error is essential for obtaining statistically valid results.
The reliability of the analysis of variance (ANOVA) depends on having sufficient error degrees of freedom (d.f.).

Step 2: Detailed Explanation:
In a Randomized Block Design with $t$ treatments and $r$ replications:
- Total degrees of freedom = $rt - 1$
- Treatment degrees of freedom = $t - 1$
- Replication (Block) degrees of freedom = $r - 1$
- Error degrees of freedom = $(r - 1)(t - 1)$
To ensure a reliable, statistically sensitive F-test for treatment effects, biometrical and agricultural research guidelines recommend that the error degrees of freedom should be at least 12 (which is identical to 12 or more).
If the error d.f. is less than 12, the estimate of experimental error variance becomes unstable, reducing the statistical power of the experiment and making it difficult to detect genuine differences between treatments.
Therefore, statements (B) and (C) are correct.

Step 3: Final Answer:
The correct statements are (B) and (C) only, corresponding to option (B).