# Completely Randomized Design (CRD)

A simplest and non–restricted experimental design, in which occurrence of each treatment has equal number of chances, each treatment can be accommodate in the plan, and the replication of each treatment is unequal is known to be completely randomized design (CRD). In this regard this design is known as unrestricted (a design without any condition) design that have one primary factor. In general form it is also known as one-way analysis of variance.

Let we have three treatments names A, B, and C placed randomly in different experimental units.

 C A C B A A B B C

We can see that from the table above:

• There may or may not be repetition of treatment
• Only source of variation is treatment
• It is not necessary that specific treatment comes in specific unit.
• There are three treatments such that each treatment appears three times having P(A)=P(B)=P(C)=3/9.
• Each treatment is appearing equal number of times (it may be unequal i.e. unbalance)
• The total number of experimental units are 9.

### Some Advantages of Completely Randomized Design (CRD)

1. The main advantage of this design is that the analysis of data is simplest even if some unit of does not response due to any reason.
2. Another advantage of this design is that is provided maximum degree of freedom for error.
3. This design is mostly used in laboratory experiment where all the other factors are in under control of the researcher. For example in a tube experiment CRD in best because all the factors are under control.

An assumption regarded to completely randomized design (CRD) is that the observation in each level of a factor will be independent from each other.

The general model with one factor can be defined as

$Y_{ij}=\mu + \eta_i +e_{ij}$

Where$i=1,2,\cdots,t$ and $j=1,2,\cdots, r_i$ with $t$ treatments and $r$ replication. $\mu$ is the overall mean based on all observation. $eta_i$ is the effect of ith treatment response. $e_{ij}$ is the corresponding error term which is assumed to be independent and normally distributed with mean zero and constant variance for each.

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Updated: Aug 2, 2015 — 11:46 pm

#### Haris Khurram

Complete my MSc statistics from Department of Statistics, Bahauddin Zakariya University, Multan. Now currently research scholar and student in M.Phil Statistics in same department.