😵‍💫 Completely Randomized Design (CRD)

• The CRD is the simplest of all the designs. In this design, treatments are allocated at random to the experimental units over the entire experimental material. In case of field experiments, the whole field is divided into a required number of plots equal size and then the treatments are randomized in these plots. Thus the randomization gives every experimental unit an equal probability of receiving the treatment.
• In field experiments there is generally large variation among experimental plots due to soil heterogeneity. Hence, CRD is not preferred in field experiments.
• In laboratory experiments and green house studies, it is easy to achieve homogeneity of experimental materials. Therefore, CRD is most useful in such experiments.

Layout of CRD

• The placement of the treatments on the experimental units along with the arrangement of experimental units is known as the layout of an experiment. For example, suppose that there are 5 treatments A, B, C, D and E. Each with 4 replications, we need 20 experimental units. Here, since the number of units is 20, a two digit random number of table will be consulted and a series of 20 random numbers will be taken excluding those which are greater than 20.
• Suppose, the random numbers are 4, 18, 2, 14, 3, 7, 13, 1, 6, 10, 17, 20, 8, 15, 11, 5, 9, 12, 16, 19. After this the plots will be serially numbered and the treatment A will be allotted to the plots bearing the serial numbers 4, 18, 2, 14 and so on.

Statistical analysis

• Let us suppose that there are ‘k’ treatments applied to ‘r’ plots. These can be represented by the symbols as follows:

Mathematical Model

y_ij = μ + α_i + ξ_ij

• i = 1,2,….k & j = 1,2,……r
• Where, y_ij is the j^th replication of the i^th treatment
  • μ = general mean effect (Common in all designs)
  • α_i = the effect due to i^th treatment
  • ξ_ij = error effect
• Source of Variability:
  • Due to treatment
  • Block
  • Error
• The null hypothesis can be verified by applying the ANOVA procedure. The steps involved in this procedure are as follows:

• N – Number of observations

ANOVA table

• If the calculated value of F > table vale of F, H₀ is rejected. Then the problem is to know which of the treatment means are significantly different.
• For this, we calculate critical difference (CD):
• CD = SED x t – table value for error d.f. at 5% LOS.
• Where,
  • SED = Standard Error of Difference between the Treatments

• The treatment means are arranged first in descending order of magnitude. If the difference between the two-treatment means is less than CD value, it will he declared as non-significant otherwise significant.

Advantages and disadvantages of CRD

• It is regarded as one-way classification and no way control or elimination.
• This design is most commonly used in laboratory experiments such as in Ag. Chemistry, plant pathology, and animal experiments where the experimental material is expected to be homogeneous.
• Applied when the experimental material is limited and homogenous, such as the soil in Pot culture experiments. However, in greenhouse experiments care has to be taken with regard to sunshade, accessibility of air along and across the bench before conducting the experiment.
• Any number of replications and treatments can be used. The number of replications may vary from treatment to treatment.
• The analysis remains simple even if information on some units are missing.
• This design provides maximum number of degrees of freedom for the estimation of error than the other designs
• The only drawback with this design is that when the experimental material is heterogeneous, the experimental error would be inflated and consequently the treatments are less precisely compared. The only way to keep the experimental error under control is to increase the number of replications thereby increasing the degrees of freedom for error.
• Local control not used in CRD.
• Error degree of freedom in CRD: N - k

Applications

• CRD is most useful in laboratory technique and methodological studies. Ex: in physics, chemistry, in chemical and biological experiments, in some greenhouse studies etc.
• CRD is also recommended in situations where an appreciable fraction of units is likely to be destroyed or fail to respond.
• CRD can be used with both equal and unequal number of repetitions.