The simplest and non-restricted experimental design, in which the occurrence of each treatment has an equal number of chances, each treatment can be accommodated in the plan, and the replication of each treatment is unequal is known to be a completely randomized design (CRD). In this regard, this design is known as an unrestricted (a design without any condition) design that has one primary factor. In general form, it is also known as a one-way analysis of variance.
There are three treatments named $A, B$, 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 a repetition of the treatment
- The only source of variation is the treatment
- Specific treatment doesn’t need to come in a specific unit.
- There are three treatments such that each treatment appears three times having P(A)=P(B)=P(C)=3/9.
- Each treatment appears an equal number of times (it may be unequal i.e. unbalanced)
- The total number of experimental units is 9.
Some Advantages of Completely Randomized Design (CRD)
- The main advantage of this design is that the analysis of data is simplest even if some unit does not respond due to any reason.
- Another advantage of this design is that it provides a maximum degree of freedom for error.
- This design is mostly used in laboratory experiments where all the other factors are under the control of the researcher. For example, in a tube experiment, CRD is best because all the factors are under control.
An assumption regarding completely randomized design (CRD) is that the observation in each level of a factor will be independent of 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 observations. $eta_i$ 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.
Read from Wikipedia: Completely Randomized Design (CRD)