Question

If in the CRD some observations are missing then also the analysis is very simple, because the missing observations are discarded and we carry out the experiment without losing the......

• A. Efficiency of the design
• B. Degrees of freedom
• C. Lower bound of the variance
• D. Unbiasedness

Hint:

CRD is highly flexible. Missing values do not require complex estimation techniques because discarding them simply leaves us with unequal replication, which still yields unbiased treatment comparisons.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Completely Randomized Design (CRD) is the simplest experimental design, where treatments are assigned to experimental units completely at random.
An advantage of CRD is its flexibility when dealing with missing observations.

Step 2: Detailed Explanation:
In more complex designs like Randomized Complete Block Designs (RCBD) or Latin Square Designs (LSD), missing observations disrupt the orthogonal structure. This requires estimating the missing values to maintain the balance of the analysis.
- In a CRD, there are no structural constraints (like blocks or rows/columns).
- If some observations are lost, we simply discard them. The design effectively becomes a CRD with unequal replications across treatments.
- The statistical analysis remains simple and straightforward. We can calculate the treatment means and the error variance using the remaining observations.
- Crucially, even with unequal replications, this analysis does not introduce bias. We still obtain unbiased estimates of the treatment effects and an unbiased estimate of the experimental error variance.
- While we do lose some degrees of freedom and some statistical power (efficiency), we do not lose the unbiasedness of our estimators.
Therefore, the correct term is unbiasedness.

Step 3: Final Answer:
In CRD, missing observations can be discarded and the analysis carried out without losing the unbiasedness of the treatment comparisons.