Completely Randomized Design Analysis: Theory, Example and Demonstration in Agri Analyze tool

 The Blog is about CRD analysis theory, example and analysis using Agri Analyze tool

Link of the MCQ for CRD design is shared in bottom

Introduction

Experimental design in agriculture is a systematic approach to planning and conducting field experiments. It involves designing the layout of experimental plots, allocating treatments and randomizing treatments to minimize bias. Common designs include Completely Randomized Design (CRD), Randomized Complete Block Design (RCBD), Factorial design, Split-plot design, and Latin square design. These designs help evaluate the effects of different factors on crops, soils, pests and other agricultural outcomes. By providing reliable and reproducible results, experimental design guides farmers and policymakers in making informed decisions to improve agricultural practices.

1.             What is Completely Randomized Design (CRD)?

            Complete Randomized Design (CRD) is a basic and widely used experimental design in agriculture and other fields. In CRD, experimental units (plots, animals, etc.) are randomly assigned to different treatment groups. Each treatment is applied to a separate group of units and all treatments have an equal chance of being assigned to any unit. This design allows researchers to compare the effects of treatments without the influence of any other variable, making it useful for studying the effects of a single factor on a response variable.

            The CRD is the simplest experimental design, based on randomization and replication principles. It's suitable for homogeneous experimental units. Treatments are randomly allocated across the entire experimental area without blocking. In field experiments, the field is divided into equal-sized plots, and treatments are randomly assigned to these plots. This design enables direct treatment comparison, making it valuable for studying single-factor effects on outcomes.

2.               When CRD is used?

The Complete Randomized Design (CRD) is primarily suitable for greenhouse, methodological, and laboratory studies where the experimental material is homogeneous. However, its use in field experiments is limited. CRD is most effective when the variation across the entire experimental unit is relatively small. In field settings where environmental variability or other factors can significantly impact results, other designs like Randomized Complete Block Design (RCBD) or Split-Plot Design are often preferred for their ability to account for and minimize such variation.

 

3.               How CRD is different from RCBD?

Complete Randomized Design (CRD) and Randomized Complete Block Design (RCBD) are two common experimental designs used in agricultural research. The main differences between the two lies in their approach to handling variability and potential sources of bias:

1.     Blocking: In CRD, there is no blocking. Treatments are assigned at random to experimental units without any consideration for grouping or blocking. In contrast, RCBD involves grouping experimental units into blocks based on similarities (e.g., soil type, field topography) and then randomizing treatments within each block. This helps account for variability within blocks and increases the precision of treatment comparisons.

2.     Precision and Control: RCBD generally provides more precise estimates of treatment effects compared to CRD. This is because blocking reduces the variability within blocks, making treatment comparisons more sensitive to real differences.

3.     Accounting for Variability: CRD assumes that all variability in the experiment is due to random factors. In RCBD, variability is partitioned into two sources: variation within blocks (which is assumed to be random) and variation between blocks (which is used to estimate the treatment effects).

4.     Efficiency: RCBD is more efficient than CRD when there is considerable variability in the experimental area or when there are known sources of variability that can be controlled by blocking.

Overall, while CRD is simpler to implement and analyze, RCBD is preferred in field experiments where there is variability that can be accounted for by blocking, leading to more reliable and precise results.

4.                ANOVA model for CRD

In a CRD, the Analysis of Variance (ANOVA) model is used to analyze the data and test the significance of treatment effects. The ANOVA model for CRD can be expressed as follows:

                                                   Y ij  =  m  +  t i +  e j  

Where,

Y i is the observation for the jth unit in the ith treatment group

m is the overall mean of the response variable

t i is the effect of the i^th treatment (i = 1, 2, ..., t)

e j is the random error associated with the observation

4.                Randomization steps in CRD

In a Complete Randomized Design (CRD), randomization of treatments is a crucial step to ensure the validity and reliability of the experiment. The steps for randomizing treatments in a CRD are as follows:

1.     Assign Numbers to Treatments: Assign a unique number to each treatment. For example, if there are 4 treatments, label them as 1, 2, 3, and 4.

2.     Random Number Generation: Use a random number generator (e.g., computer software, random number table) to generate a random sequence of numbers corresponding to the treatments. This random sequence will determine the order in which treatments are assigned to experimental units.

3.     Assign Treatments: Assign treatments to experimental units according to the random sequence generated. Treatments should be assigned sequentially in the order given by the random sequence.

4.     Ensure Balance: Ensure that each treatment is assigned an equal number of times and that each experimental unit receives only one treatment.

5.     Record and Implement: Record the randomization process and implement it in the actual experiment. This helps maintain the integrity of the randomization and ensures that the experiment is conducted as planned.

By following these steps, the randomization of treatments in a CRD helps minimize bias and ensures that any observed differences among treatments are due to the treatments themselves and not to the way they were assigned.

5.                Analysis steps for CRD

1.     Calculate Means: Calculate the mean of each treatment group, as well as the overall mean of all observations.

2.     Calculate Sum of Squares: Calculate the total sum of squares (SST), sum of squares due to treatments (SST) and sum of squares due to error (SSE).

3.     Calculate Degrees of Freedom: Determine the degrees of freedom for treatments and error.

4.     Calculate Mean Squares: Calculate the mean squares for treatments (MST) and error (MSE) by dividing the sum of squares by their respective degrees of freedom.

5.     Calculate F-Statistic: Calculate the F-statistic by dividing MST by MSE.

6.     Determine Significance: Use the F-statistic to determine the significance of the treatment effects. Compare the calculated F-value to the critical F-value from the F-distribution table at a chosen significance level (e.g., 0.05). If the calculated F-value is greater than the critical F-value, reject the null hypothesis and conclude that there are significant differences among the treatment means.

7.     Perform Post-hoc Tests (if needed): If the F-test indicates significant differences among treatment means, perform post-hoc tests (e.g., Tukey's HSD, LSD) to determine which specific treatments differ from each other.

8.     Interpret Results: Interpret the results of the analysis, including the significance of treatment effects and any pairwise differences between treatments.

9.     Report Findings: Present the results of the analysis in a clear and concise manner, including tables or graphs to display the data and statistical findings.

By following these steps, researchers can effectively analyze data from a CRD and draw valid conclusions about the effects of treatments on the response variable.

4.                ANOVA outline for CRD

Here's a brief outline of the ANOVA procedure for a Complete Randomized Design (CRD):

4.                Example of CRD

Consider the following data on gains in weight (kg/6 weeks) due to A, B, C, D and E, the five different feeds fed to twenty Kankrej heifers, four animals in each group.

A	B	C	D	E
20.0	21.5	12.8	16.5	17.2
18.5	22.2	14.2	14.8	17.9
18.2	24.6	15.0	17.6	21.3
20.3	23.7	16.0	18.1	20.6

 

Solution:

In order to check this null hypothesis, we are required to compare the Calculate F value (18.259) with Table F value (3.05). As the Calculated F value is greater than Table F value our results are significant at 5 % level of significance. Further we can test for 1 % level by comparing Calculate F value (18.259) with Table F value (4.89), so result is also significant at 1 % level of significance, and we reject our null hypothesis.

This mean that mean performance of all the treatment is not same. This raises the question that which treatment gives a better Feed. In order to get this answer, we need to perform LSD test.

LSD TEST (FOR MEAN COMPARISON):

Step 2: Calculate the treatment means and arrange them in ascending order

The treatment mean is obtained by dividing treatment total with number of replications

B	A	E	D	C
23.00	19.25	19.25	16.75	14.50

Conclusion

The ANOVA results reveal that the treatment component is significant at 1 % level of significance. The LSD test reveals that highest yield was observed for treatment B and none of the treatments was at par with it.

Feeds A and E are not significantly different from each other. While feeds B, C and D significantly differed from each other and with feeds A and E also. Feed B is the best feed among the five-feed tried.

Steps to perform analysis of CRD in Agri Analyze

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

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

Step 3: Click on ANALYTICAL TOOL

Step 4: Click on DESIGN OF EXPERIMENT

Step 5: Click on CRD ANALYSIS

Step 6: Click on ONE FACTOR CRD ANALYSIS

Step 7: Select CSV file.

Step 8: Select treatment 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.

REFERENCES

Gomez, K. A., & Gomez, A. A. (1984). Statistical Procedures for Agricultural Research. John wiley & sons. 8-13.

This post is written by:

Darshan Kothiya

Content Writer

Agri Analyze

MCQ questions for CRD: