Question

What is the Error Degree of Freedom for the experiment consisting of Eight treatments and with three replications in RBD.

• A. 14
• B. 16
• C. 12
• D. 23

Hint:

For any RBD, simply subtract 1 from the number of treatments ($8 - 1 = 7$) and subtract 1 from the number of replications ($3 - 1 = 2$), then multiply the results: $7 \times 2 = 14$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In agricultural and forestry research, the Randomized Block Design (RBD) is a standard experimental design used to control for a single source of environmental variation (such as soil fertility gradients or slope direction) by grouping experimental units into homogenous blocks (replications).
Key Formula or Approach:
For an RBD containing $t$ treatments and $r$ replications (blocks), the degrees of freedom (DF) for the Analysis of Variance (ANOVA) are calculated as:
- Total DF:
\[ \text{Total DF} = (t \times r) - 1 \]
- Treatment DF:
\[ \text{Treatment DF} = t - 1 \]
- Replication (Block) DF:
\[ \text{Replication DF} = r - 1 \]
- Error DF:
\[ \text{Error DF} = (t - 1) \times (r - 1) \]

Step 2: Detailed Explanation:
Let us calculate the Error Degrees of Freedom using the values provided in the question:
- Number of treatments ($t$) = 8
- Number of replications ($r$) = 3
Using the Error DF formula:
\[ \text{Error DF} = (t - 1) \times (r - 1) \]
Substitute the values into the formula:
\[ \text{Error DF} = (8 - 1) \times (3 - 1) \]
\[ \text{Error DF} = 7 \times 2 \]
\[ \text{Error DF} = 14 \]
Therefore, the error degrees of freedom is 14, matching Option (A).

Step 3: Final Answer:
The Error Degree of Freedom for the experiment is 14.