# Completely Randomized Design

**Completely Randomized Design**

Completely randomized design is one of the most competent statistical tools which are widely used in solving the statistical as well as management problems. This design is perfect in analyzing and calculating the experimental designs without fail. The hands on experience help the professionals to use these designs for problem solving and also in improving the current infrastructural problems.

Designs of experiments include the study of all the designs where variation is present. Design of experiment is a discipline that has a very broad application across all the social and natural sciences.

Completely randomized design can be defined as studying effects of a primary factor with other factors not taken into consideration in the design of experiments. Completely randomized design falls within the category of true random number generation. It is the simplest form of design.

In completely randomized design, subjects are assigned to various groups at random. The most reliable method of creating the homogeneous treatment groups is the using of randomization and also without the involving of any judgements. Completely randomized designs are analyzed by one way ANOVA.

To label each subject and also to assign subjects to treatment groups, one standard group is applied. It is also used with a table of random numbers with the aim to select from the labelled subjects in complementary randomized design. In completely randomized design, replications of treatments are assigned completely at random to independent experimental subjects and adjacent subjects could potentially have the same treatment.

Under totally randomized designs, random assignment of primary factor levels to the units for experiments takes place. Randomizing means ‘run sequence’ of units to be experimented is decided randomly. Provided the sample size is adequate, the risks associated with random allocation are calculable and hence can be managed down to an acceptable level.

To quote an example, suppose 3 levels of primary factor are there with 1 level to run twice. Then, there would be six different ways to sequence the experimental trials (or 6 factorial sequences of run). In common practice, normally a program of computer performs the randomization. Random no. tables can also help in randomization. Most of the CRD with 1 primary factor can be defined by three numbers. These numbers are

k = No. of Factors,

L = No. of levels and

N = No. of replications.

A completely randomized design is the simplest type of randomization scheme in which treatments are assigned to units completely by chance. In addition, units should be run in random order throughout the experiment. The completely randomized design has several advantages:

• It is completely flexible. Any number of treatments can be investigated. Each treatment can have any number which should be more than one unit although balance (an equal number of units for each treatment) is desirable.

• The statistical analysis is straightforward.

• The analysis remains simple even if observations from some units are missing.

There is only one disadvantage to the CRD. Unrestricted randomization means that units that receive one treatment may be inherently different from units that receive other treatments. Any variation in units shows up in the experimental error sum of squares. Unless the units are very similar, a CRD will have larger experimental error than other designs.

There is one thing that compensates partially for this. For a given number of observations, a completely randomized design has the largest degrees of freedom for error. Although the sum of squares error may be inflated by the natural variability in units, this sum of squares will be divided by the largest degrees of freedom possible to produce the mean square error.

Given these advantages and disadvantages, a CRD is most appropriate when:

• Experimental units are similar.

• Several units may be destroyed or fail to respond.

• It is a relatively small experiment.

Complementary randomized design is used in six sigma also. Random does not mean haphazard, and great care must be taken that appropriate random methods are used as it allows the experimenter to control two sources of variations.

This design is widely used as a competent statistical tool. Apart from the statistics professionals, the six sigma professionals are also accustomed with this particular tool. The green belt professionals need to learn this during their course of a week or two. They also get hands on experience on the same so that they can apply it in practical situations. Completely randomized design has significant advantages that are used in different fields so that the error part is minimized without much effort and the company infrastructure moves towards complete enhancement.