Question

In a completely randomized design with 5 treatments, treatments 1 and 2 are replicated 4 times each and treatments 3, 4 and 5 are replicated 3 times each. The degrees of freedom for error will be:

• A. 6
• B. 12
• C. 13
• D. 16

Hint:

Exam Tip:
In CRD:

• Total df = \(N - 1\).
• Treatment df = \(t - 1\).
• Error df = \(N - t\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a completely randomized design (CRD), the degrees of freedom for error are: \[ \text{df}_{\text{error}} = N - t \] where \(N\) is the total number of observations and \(t\) is the number of treatments.

Step 2: Key Formula or Approach:
Total number of observations: \[ N = 4 + 4 + 3 + 3 + 3 = 17 \] Number of treatments: \[ t = 5 \] So, \[ \text{df}_{\text{error}} = 17 - 5 = 12 \]

Step 3: Detailed Explanation:
The error degrees of freedom represent the number of independent pieces of information available to estimate the error variance.
In CRD, \(\text{df}_{\text{error}} = N - t\).
Here, \(N = 17\) and \(t = 5\), so \(\text{df}_{\text{error}} = 12\).

Step 4: Final Answer:
Therefore, option (B) is correct.