Complete Random Design (CRD)

A completely randomized design (CRD) is one where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment.

In CRD, as the name suggests, treatments are assigned completely randomly so that each treatment unit gets the same chance of receiving any one treatment. This is suitable only for the experiments such as laboratory experiments or greenhouse studies etc, where the experiment material is homogeneous and not for heterogeneous studies.

All CRDs with one primary factor are designed by 3 numbers:

• k, indicates number of factors
• L, indicates number of levels
• n, indicates number of replications

Total sample size  which indicates number of runs (N=k*L*n)

For example:

• k=1 factor
• L = 4 levels of that single factor (called "1", "2", "3" and "4")
• n = 3 replications per level
• N =L*n = 12 runs

Features of Complete Random Design (CRD):

• The whole field is divided directly into plots (product of replications=treatments).
• In CRD, treatment-wise randomization is done.
• Local Control is not adopted in this case.
• It is divided into 2 component divisions.
• Analysis in CRD is very easy and simple.

Randomization Procedure in Complete Random Design (CRD):

• Each replicate is randomized separately.
• Each treatment has the same probability of being assigned to a given experimental unit within a replicate.
• Each treatment must appear at least once per replicate.

For Example- Given four fertilizer rates applied to ‘Amidon’ wheat and three replicates of each treatment.

where, A = 0 KG N/ha, B = 50 KG N/ha, C = 100 KG N/ha, D = 150 KG N/ha

Fixed vs Random Effect in Complete Random Design (CRD):

• ANOVA assumes the independent variable is fixed in Fixed Effect, while in Random Effect, it assumes an independent variable is random.
• Fixed effects probably produce smaller standard errors, while the Random effect produces larger standard errors.
• The fixed effect has a large number of parameters, whereas the random effect has the small number of parameters.

Advantages of Complete Random Design (CRD):

• It is simple and easy.
• It provides a maximum number of degrees of freedom.
• Flexibility: CRD is a flexible experimental design that allows for easy modifications and adjustments, which can be particularly useful when dealing with unforeseen circumstances or changing research needs.
• Unbiased: CRD eliminates any possible bias in the experimental setup, since treatments and control groups are randomly assigned. This means that all factors other than the treatments are held constant, and any observed differences between the groups can be attributed solely to the treatment.
• Statistical efficiency: CRD is a statistically efficient design, meaning that it requires the smallest sample size to obtain the desired level of statistical power. This can result in significant cost savings and reduced experimental time.
• Independence: Each experimental unit in CRD is completely independent of all other units. This makes it easier to identify and measure treatment effects, since each unit is unaffected by the behavior or characteristics of other units.
• Wide applicability: CRD can be used in a wide range of fields, from agriculture to medicine to psychology, making it a versatile and widely applicable experimental design.

Disadvantages of Complete Random Design (CRD):

• It is less accurate than other designs.
• It reduces precision.
• It increases experimental errors.
• Lack of control: With CRD, there is no control over external factors that may influence the experimental outcomes. This can make it difficult to isolate the effects of the independent variable on the dependent variable.
• Inefficient use of resources: In some cases, CRD may require a large sample size to achieve statistical power, which can be inefficient in terms of time, resources, and cost.
• Limited ability to detect interactions: CRD is not ideal for detecting interactions between variables. This is because interactions may only be detected when certain variables are combined, and CRD treats each variable as independent.
• Homogeneity assumptions: CRD assumes homogeneity of variances and covariances across treatment groups, which may not always be true. This can lead to inaccurate results and conclusions.
• May not be suitable for complex experiments: CRD is a relatively simple experimental design and may not be suitable for complex experiments that involve multiple variables, factors, and treatments.