Question

Randomization in designed experiments ensures that

• A. errors are independent
• B. error variances are homogeneous
• C. error variance is stable
• D. experimental units are homogeneous

Hint:

Remember this direct matching of principles to their functions:
- Randomization $\rightarrow$ Independence of errors
- Replication $\rightarrow$ Estimation of error variance
- Local Control $\rightarrow$ Reduction of error variance

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The three basic principles of experimental design introduced by Fisher are replication, randomization, and local control.

Step 2: Detailed Explanation:
Let us analyze the main function of each principle:
- Replication: Allows us to estimate the experimental error variance and increases the precision of the treatment estimates.
- Randomization: Ensures that treatments are allocated to experimental units by chance. This eliminates subjective bias and ensures that the experimental errors are independent random variables, validating the use of standard probability-based tests (like the $F$-test).
- Local Control: Groups homogeneous experimental units into blocks to reduce the overall experimental error.
Therefore, randomization specifically ensures that errors are independent.

Step 3: Final Answer
The correct option is (A).