Question

In RCBD we may assume that the treatment are fixed and the blocks are random, such a model is called

• A. Random effect model
• B. Fixed effect model
• C. Mixed effect model
• D. Regression model

Hint:

In ANOVA:
- All factors fixed $\rightarrow$ Fixed model
- All factors random $\rightarrow$ Random model
- Combination of fixed and random $\rightarrow$ Mixed model

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In the Analysis of Variance (ANOVA) for experimental designs, linear models are classified into three types based on the assumptions made about the treatment and environmental factors: Fixed Effects Model (Model I), Random Effects Model (Model II), and Mixed Effects Model (Model III).

Step 2: Detailed Explanation:
Let us analyze the assumptions for the Randomized Complete Block Design (RCBD):
The linear model for a standard RCBD is:
\[ y_{ij} = \mu + \tau_i + \beta_j + \epsilon_{ij} \]
where \( \tau_i \) represents the treatment effect and \( \beta_j \) represents the block effect.
- Fixed Effects Model: Assumes both treatments and blocks are fixed factors (i.e., we are only interested in testing the specific treatments and blocks included in the experiment).
- Random Effects Model: Assumes both treatments and blocks are random samples from larger populations of treatments and blocks.
- Mixed Effects Model: Assumes at least one factor is fixed and at least one is random.
- In agricultural experiments, treatments (e.g., fertilizer rates, crop varieties) are typically selected deliberately, making them fixed effects.
- Blocks (e.g., locations, fields, batches) are often assumed to be random samples from a larger population of environments, making them random effects.
Because this design contains both fixed and random effects, it is classified as a mixed effect model.

Step 3: Final Answer:
An RCBD model with fixed treatments and random blocks is called a Mixed effect model.