Question

If there are 6 treatments with 4 replications to each, the error degree of freedom for RCBD will be

• A. 18
• B. 20
• C. 15
• D. 24

Hint:

RCBD Error df formula: $(t-1)(r-1) = (6-1)(4-1) = 5 \times 3 = 15$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In a Randomized Complete Block Design (RCBD), total experimental degrees of freedom are partitioned into replication, treatment, and error degrees of freedom.
Key Formula or Approach:
\[ \text{Error Degrees of Freedom} = (t - 1)(r - 1) \]
where \(t\) is the number of treatments and \(r\) is the number of replications.

Step 2: Detailed Explanation:
Given experimental parameters:
- Number of treatments: \(t = 6\)
- Number of replications: \(r = 4\)
Computing degrees of freedom:
- Treatment df: \(t - 1 = 6 - 1 = 5\)
- Replication (Block) df: \(r - 1 = 4 - 1 = 3\)
- Error df: \((t - 1)(r - 1) = 5 \times 3 = 15\)
- Total df: \(t \cdot r - 1 = 6 \times 4 - 1 = 23\).

Step 3: Final Answer:
Therefore, the error degree of freedom for RCBD is 15, matching option (C).