Randomized Complete Block Design (RCBD): Theory, Example and Demonstration in Agri Analyze tool

 This blog explains RCBD design in detail, guides step by step to perform analysis and demonstrates its analysis online using Agri Analyze tool. Link of the MCQ is shared in bottom! (Reading time 15 min)

Introduction

            Experimental design is a systematic approach in scientific research, essential for investigating relationships among variables. It ensures valid and interpretable results through randomization, replication and control. Randomization distributes extraneous variables evenly, reducing bias. Replication increases reliability and precision by accounting for variability within experimental units. Control ensures that observed differences are due to the independent variable. Designs range from simple completely randomized designs to complex ones like randomized complete block designs, factorial designs and Latin squares. These designs help isolate variable effects and understand their interactions. Effective experimental design is crucial for drawing valid conclusions and advancing scientific knowledge across various fields.

Randomized Complete Block Design (RCBD)

            Randomized Complete Block Design (RCBD) is a fundamental experimental design used extensively in scientific research to control for variability within experimental units. In RCBD, each block contains all treatments, with random assignment within blocks, controlling for variability and ensuring comprehensive treatment comparison. Hence, it is called "Randomized Complete Block Design." This design reduces experimental error and enhances the precision of treatment comparisons by accounting for block-to-block variability. RCBD is particularly useful in experiments with known or suspected gradients in conditions, such as soil fertility in agricultural studies. It is essential for drawing valid inferences about treatment effects while minimizing the influence of extraneous factors.

When RCBD is used?

            The RCBD is employed in agricultural research under specific conditions to achieve reliable and precise results. Here are scenarios when RCBD is used:

1.     Heterogeneous Experimental Units: When there is significant variability within the experimental field, such as differences in soil fertility, moisture, or topography, RCBD helps control this variability by grouping similar units into blocks.

2.     Known Gradients: When there are known gradients in the experimental area (e.g., fertility gradients across a field), RCBD is used to ensure that each treatment is tested across all levels of the gradient, reducing the impact of these gradients on treatment comparisons.

3.     Multiple Treatments: When comparing multiple treatments (e.g., different crop varieties, fertilizers, or pest control methods), RCBD ensures that each treatment is equally represented within each block, allowing for accurate comparison.

1.     Limited Experimental Units: In cases where the number of experimental units is limited, RCBD maximizes the use of available units by reducing experimental error, thus enhancing the precision of the results.

2.     Small-Scale Trials: For small-scale trials where variability within the experimental area can significantly impact results, RCBD provides a robust method to control for this variability.

Assumptions of RCBD

            The RCBD operates under several key assumptions to ensure valid and reliable results:

1.     Homogeneity within Blocks: The experimental units within each block are assumed to be homogeneous, meaning they are similar in terms of characteristics that could affect the response variable (e.g., soil fertility, moisture levels).

2.     Independence of Observations: Observations from different experimental units are assumed to be independent of each other. The response of one unit does not influence the response of another.

3.     Additivity of Effects: The effects of blocks and treatments are additive, meaning there are no interactions between blocks and treatments.

4.     Random Assignment: Treatments are randomly assigned to experimental units within each block to ensure unbiased estimates of treatment effects.

5.     Normality: The response variable for each treatment is assumed to be normally distributed within each block.

6.     Equal Variance: The variance of the response variable is assumed to be the same for all treatments within each block.

7.     No Missing Data: It is assumed that there are no missing data points. Each treatment is represented in every block.

Randomization steps in RCBD

            Randomization in a Randomized Complete Block Design (RCBD) is a crucial step to ensure unbiased allocation of treatments to experimental units within each block. Here are the detailed steps for randomization in RCBD:

1.     Identify the Treatments: List all the treatments to be tested in the experiment. Let's assume there are t treatments

2.     Define the Blocks: Identify and define the blocks based on homogeneous characteristics. Each block will contain all the treatments. Let's assume there are r blocks (replications).

3.     Assign Treatments Randomly within Each Block: To randomly assign treatments within each block in an RCBD, list all treatments and use a randomization method such as random number tables, computer software, or drawing lots. Document the random allocation for each block to ensure clear and unbiased treatment distribution across the experimental units.

4.     Record the Assignment: Document the random allocation of treatments for each block to ensure the layout plan is clear and can be followed accurately during the experiment.

5.     Repeat for All Blocks: Repeat the randomization process for each block until all treatments have been randomly assigned to plots within every block.

6.     Verify Randomization: Ensure that each treatment appears once in every block and that the allocation is indeed random. This can be done by checking the documentation or using software outputs.

7.     Create a Layout Plan: Develop a visual representation or map of the experimental layout showing the randomized assignment of treatments within each block.

Example of RCBD

            Ten wheat varieties were put under yield trial against local in randomizes block design with four replications at the Vijapur farm. Observed yield data is given below.

Genotypes	Replications				Total of genotype	Mean of genotype
	R-1	R-2	R-3	R-4
Haura	148	132	148	132	560	140
HY-12	155	156	157	160	628	157
HY-65-4	112	136	126	150	524	131
HY-11-6	112	114	100	118	444	111
HY-12-5-3	124	125	126	125	500	125
HY-5-7-2	92	94	98	96	380	95
HY-11-8	116	124	130	134	504	126
Kalyan sona	115	121	122	126	484	121
Sonalika	131	131	132	130	524	131
GW-24	145	149	150	156	600	150
Rep total	1250	1282	1289	1327	5148

Conducting LSD test for multiple mean comparison

1.     Arrange varieties means in descending order, find difference (d) between two consecutive means and follow procedure given below:

Varieties	Mean
HY-12	157
GW-24	150
Haura	140
HY-65-4	131
Sonalika	131
HY-11-8	126
HY-12-5-3	125
Kalyan sona	121
HY-11-6	111
HY-5-7-2	95

2.     Find difference between two consecutive means

3.     d= 157-150 =7. If d >= CD, then both means are significantly different. There is no need to find d between HY-12 and GW-24. If d < CD, then both means are not significantly different OR we can say both are at par. Here, both varieties are significantly at par.

4.     But d = 157 (HY-12) – 140 (Haura) =17, Here d >= CD, then both means are significantly different.

5.     d = 150 (GW-24) – 140 (Haura) =10, Here d >= CD, then both means are significantly different.

6.     d = 140 (Haura) – 131 (HY-65-4) = 9, Here d < CD, then both means are not significantly different. Same for Sonalika, these varieties are significantly at par.

7.     Follow same procedure to exhaust all means.

8.     Final LSD test for varieties given as under:

Varieties	Mean	Group
HY-12	157	a
GW-24	150	a
Haura	140	b
HY-65-4	131	bc
Sonalika	131	bc
HY-11-8	126	cd
HY-12-5-3	125	cd
Kalyan sona	121	d
HY-11-6	111	e
HY-5-7-2	95	f

Steps to perform analysis of RCRD in Agri Analyze

Step 1: To create a CSV file with columns for Genotype and Yield (Gain).

The link of the entire data set

Step 2: Go with Agri Analyze site.  https://agrianalyze.com/Default.aspx

Step 3: Click on ANALYTICAL TOOL

Step 4: Click on DESIGN OF EXPERIMENT

Step 5: Click on RCRD ANALYSIS

Step 6: Click on ONE FACTOR RCRD ANALYSIS

Step 7: Select CSV file.

Step 8: Select treatment, replication and dependent variable (e.g., Gain).

Step 9: Select a test for multiple comparisons, such as the Least Significant Difference (LSD) test, to determine significant differences among groups. Same as for Duncan’s New Multiple Range Test (DNMRT), Tukey’s HSD Test.

Step 10: After submit download analysis report.

Output File Snip

Link of the output file

REFERENCES

Gomez, K. A., & Gomez, A. A. (1984). Statistical Procedures for Agricultural Research. John wiley & sons. 25-30.

See Also:

Completely Randomized Design Analysis using Agri Analyze

MCQ questions of RCBD

The blog is written by 

Darshan Kothiya