Question

For the analysis of variance of data from plot sampling in a CRD with 't' treatments, 'r' replications and 's' sampling units per plot, sampling error will be

• A. (r-1)(s-1)
• B. rt(s-1)
• C. r(st-1)
• D. t(r-1)(s-1)

Hint:

ANOVA in CRD with sub-sampling:
- Treatment error: (t-1).
- Sampling error: rt(s-1).
- Total df: trs - 1.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question tests knowledge of ANOVA in experimental designs.

Step 2: Key Formula or Approach:
In a CRD (Completely Randomized Design) with t treatments, r replications, and s sampling units per plot:
- Total observations = t × r × s.
- Degrees of freedom for sampling error = t × r × (s-1).

Step 3: Detailed Explanation:
The sampling error is the variation among sampling units within the same plot.
The degrees of freedom for sampling error = rt(s-1).
Option A: (r-1)(s-1) is incorrect.
Option C: r(st-1) is incorrect.
Option D: t(r-1)(s-1) is incorrect.
Thus, the correct answer is rt(s-1).
Final Answer:
Thus, the sampling error is rt(s-1), which corresponds to option (B).
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