A completely randomised design is based on the principles of ______ and randomisation only.
replication
Understanding Completely Randomized Design (CRD) Principles
A Completely Randomized Design (CRD) is one of the simplest experimental designs used in statistics. It involves randomly assigning experimental units to different treatment groups. The key idea is that every experimental unit has an equal chance of receiving any of the treatments.
Core Principles of Experimental Design
There are generally considered to be three fundamental principles of good experimental design:
- Randomization: This principle involves assigning treatments to experimental units randomly. Randomization helps to average out the effects of extraneous factors that we are not interested in or cannot control, thus preventing bias.
- Replication: This principle involves repeating the treatment on multiple experimental units. Replication increases the precision of the experiment, allows for estimation of experimental error, and provides a basis for testing the significance of treatment differences.
- Local Control: This principle involves grouping experimental units into blocks or other homogeneous groups before assigning treatments. Local control helps to reduce the variation within groups, making it easier to detect treatment effects. Designs that use local control include the Randomized Complete Block Design (RCBD).
Applying Principles to Completely Randomized Design
The question asks about the principles upon which a Completely Randomized Design (CRD) is based, specifically stating "randomisation only" and one other principle. Let's examine which of the core principles apply to CRD:
- Randomization: Yes, random assignment of treatments to all experimental units is the defining feature of CRD. This is explicitly mentioned in the question.
- Replication: Yes, in a CRD, treatments are typically applied to multiple experimental units (replicates). This is essential for estimating variability and performing statistical tests.
- Local Control: No, CRD does not incorporate local control. There is no grouping of experimental units into blocks based on homogeneity before randomization. The randomization is applied directly to all units.
Therefore, a Completely Randomized Design (CRD) is based on the principles of randomisation and replication.
Analyzing the Options based on CRD Principles
Let's look at the given options in the context of the principles of a Completely Randomized Design:
- Option 1: divisibility - This is not a standard principle of experimental design.
- Option 2: compounding - This is not a standard principle of experimental design. It might relate to confounding, which randomization helps to prevent, but it's not a foundational principle in the positive sense.
- Option 3: local control - While a principle of experimental design, CRD specifically *does not* use local control.
- Option 4: replication - This is a standard principle of experimental design and is fundamental to CRD alongside randomisation.
Based on this analysis, the principle that completes the statement "A completely randomised design is based on the principles of ______ and randomisation only" is replication.
The Completely Randomized Design relies solely on randomisation and replication to ensure validity and power, without using techniques like blocking (local control).
| Principle | Completely Randomized Design (CRD) | Designs with Local Control (e.g., RCBD) |
|---|---|---|
| Randomization | Yes | Yes (within blocks) |
| Replication | Yes | Yes (across blocks) |
| Local Control | No | Yes (using blocks) |
Conclusion on CRD Principles
The question correctly identifies randomisation as one principle of CRD. The other principle, crucial for estimating error and validity, is replication. CRD is characterized by applying these two principles across all experimental units without any form of blocking or grouping (local control).
Revision Table: Key CRD Concepts
| Concept | Description |
|---|---|
| Randomization | Every experimental unit has an equal chance of receiving any treatment. |
| Replication | Repeating each treatment on multiple units. |
| Local Control | Not used in basic CRD. No grouping of units before randomization. |
| Suitability | Best for homogeneous experimental units (e.g., lab experiments, greenhouse studies). |
Additional Information on Completely Randomized Design
While simple, the Completely Randomized Design is most effective when the experimental units are relatively homogeneous. If there are known sources of variation among the units that could affect the response (e.g., different locations in a field, different batches of material), designs that incorporate local control, such as the Randomized Complete Block Design (RCBD) or Latin Square Design, might be more appropriate to reduce experimental error.
In CRD, the total variation in the response is typically partitioned into variation due to the treatments and variation due to random error. Replication allows us to estimate this random error and determine if the observed differences between treatments are statistically significant or just due to chance variability.
Important Questions from Sampling Theorems
In the construction of cost of living index, commodities are selected by:
If 4, 5, 6, 6, 6, 6, 6, 6, 6, 7 be a random sample from a Poisson population with parameter λ, then an unbiased estimate of λ is:
The data taken from the publication "sankhya" will be considered as:
A sample of 30 latest returns on UTI stock reveals a mean return of $4 with a sample standard deviation of $0.13. The estimated standard error of the sample mean is:
In a cluster sampling wherein the units within same cluster are highly correlated, suppose \(S_w^2\) represents the variance within the clusters and \(S_b^2\) between clusters, then which option is correct?
