# Experimental Design And Its Application

1. The various terminologies required to build the concept ( experimental units, treatments, experimental error, blocks).
2. The three principles of Experimental Design i.e. Randomisation, Replication, and Local Control
3. The 4 main Experimental Designs i.e. CRD, RBD, LSD and Factorial Designs.

Experiments answer questions. Experiments help us develop mathematical relationships between the various experimental units, minimize errors and draw various conclusions.

Experiments can be controlled. Having that control allows us to make stronger inferences about the nature of differences that we see in the experiment. Whereas, observational data are not changed or modified by any attempt on the part of an experimenter. So, it is often difficult to assign cause and effect by studying observational data which is easier in the case of experimental data.

An experimental design is defined as an effective procedure to plan experiments such that the data can be analyzed so as the results yield objective and valid conclusions.

In the words of Allen L. Edwards, “The Experimental design is called a randomized group design. The essential characteristic of this design is that subjects are randomly assigned to the experimental treatments or vice versa.”

### TERMINOLOGY

Treatments, units and assignment method specify the experimental design.

1. Experimental Units
An experimental unit is a person or object that will be studied by the researcher. This is the smallest unit of analysis in the experiment from which the data will be collected. For example, depending on the objectives, experimental or sampling units can be individual persons, students in a classroom, patients from a doctor’s office and so on.

2. Treatments
Various objects of comparison in a comparative experiment. It is the factor about which the experimenter makes inferences.
Many experiments are conducted to establish the effect of one or more variables (independent) on a response (dependent variable). The independent variables are factors or treatments, such as different ways of packaging merchandise, different advertisement channels and so on. The values of a response are supposed to reflect the effects of different treatments.

3. Experimental Error
It is the random variation present in all experimental results. Different experimental units give different responses to the same treatment. Also, if we apply the same treatment again and again to an experimental unit, we often get different results every time. Such variations are due to random or chance factors beyond human control.

4. Blocks
The term block comes from the agricultural heritage of experimental design where a large block of land was selected for the various treatments, that had uniform soil, drainage, sunlight, and other important physical characteristics. Homogeneous clusters improve the comparison of treatments by randomly allocating levels of the treatments within each block. These blocks are amongst themselves.

### THE THREE PRINCIPLES Replication: Although randomization helps to ensure that treatment groups are as similar as possible, the results of a single experiment, applied to a small number of objects or subjects, should not be accepted without question. Randomly selecting two individuals from a group of four and applying a treatment with “great success” generally will not impress the public or convince anyone of the effectiveness of the treatment.

To improve the significance of an experimental result, replication, the repetition of an experiment on a large group of subjects, is required. If a treatment is truly effective, the long-term averaging effect of replication will reflect its experimental worth.

If it is not effective, then the few members of the experimental population who may have reacted to the treatment will be negated by the large numbers of subjects who were unaffected by it. Replication reduces variability in experimental results, increasing their significance and the confidence level with which a researcher can draw conclusions about an experimental factor

Randomisation: As it is generally extremely difficult for experimenters to eliminate bias using only their
expert judgment, the use of randomization in experiments is common practice. In a randomized
experimental design, objects or individuals are randomly assigned (by chance) to an experimental group. Using randomization is the most reliable method of creating homogeneous treatment groups, without
involving any potential biases or judgments.

Local Control: The process of reducing the experimental error by dividing the relatively heterogeneous experimental area (field) into homogeneous blocks (due to physical contiguity as far as field experiments are concerned) is known as local control. Local control also increases the efficiency of the design.

### COMPLETELY RANDOMISED DESIGN or 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. For the CRD, any difference among experimental units receiving the same treatment is considered as an experimental error.

Hence, CRD is appropriate only for experiments with homogeneous experimental units, such as laboratory experiments, where environmental effects are relatively easy to control. For field experiments, where there is generally large variation among experimental plots in such environmental factors as soil, the CRD is rarely used.

It is the simplest of all designs. The Local Control principle is missing in this design.

Layout
Let us suppose, we have g treatments to compare and N units to use in our experiment. For a completely randomized design:

1. Select sample sizes n1, n2, . . . , ng with n1 + n2 + · · · + ng = N.
2. Choose n1 units at random to receive treatment 1, n2 units at random from the N − n1 remaining to receive treatment 2, and so on.

This is best suited for the experiments with a small number of treatments.

### RANDOMISED BLOCK DESIGN or RBD

The randomized block design (RBD) is one of the most widely used experimental designs in forestry research. The design is especially suited for field experiments where the number of treatments is not large and there exists a conspicuous factor based on which homogenous sets of experimental units can be identified. The primary distinguishing feature of the RBD is the presence of blocks of equal size, each of which contains all the treatments.

In a block design, experimental subjects are first divided into homogeneous blocks before they are randomly assigned to a treatment group. If, for instance, an experimenter had reason to believe that age might be a significant factor in the effect of a given medication, he might choose to first divide the experimental subjects into age groups, such as under 30 years old, 30-60 years old, and over 60 years old.

Then, within each age level, individuals would be assigned to treatment groups using a completely randomized design. In a block design, both control and randomization are considered.

Layout
Let us consider five treatments A, B, C, D, and E each replicated four times. We divide the whole experimental area into four relatively homogeneous blocks and each block into five units. Treatments are then allocated at random to the plots of a block, fresh randomization being done for each block. In general, for v treatments each being replicated r times, we will have r blocks and each block will be divided into v units. So, we will have rv=N experimental units in the field.

### LATIN SQUARE DESIGN OR LSD

A Latin square is a table filled with n different symbols in such a way that each symbol occurs exactly
once in each row and exactly once in each column. Here are two examples.  A Latin square design is a method of placing treatments so that they appear in a balanced fashion within a square block or field. Treatments appear once in each row and column. Replicates are also included in this design.

• Treatments are assigned at random within rows and columns, with each treatment once per row and once per column.
• There are equal numbers of rows, columns, and treatments.
• Useful where the experimenter desires to control variation in two different directions.

Layout
Suppose we have 4 treatments A, B, C and D, then it means that we have Number of treatments = Number of Rows = Number of Columns = 4
In general, if we have v treatments, then we will need the same number of rows and columns.

There will be v2 be experimental units in the field. The v treatments are then allocated at random to these
rows and columns in such a way that every treatment occurs once and only once in each row and each
column.

For example, if we are interested in studying the m types of fertilizers on the yield of a certain variety of wheat, it is customary to conduct the experiments on a squared field with m2 experimental units of equal area and to associate treatments with different fertilizers and row and column effects with variations in fertility of soil.

### FACTORIAL DESIGN

Suppose an investigator is interested in examining three components of a weight loss intervention. The
three components are

1. Keeping a food diary ( yes or no) denoted by F;
2. Increasing activity (yes or no) denoted by A;
1. Home visit (yes or no) denoted by H.

The investigator plans to manipulate each of these components experimentally. Thus, each becomes an
independent variable.

The investigator plans to use a factorial experimental design. In factorial experiments, the effects of several factors of variation are studied and investigated simultaneously, the treatments being all the combinations of different factors under study. In these experiments, an attempt is made to estimate the effects of each of the factors and also the interaction effects, i.e., the variation in the effect of one factor as a result to different levels of other factors.

In the above example, each independent variable is a factor in the design. As there are three factors and
each factor has two levels, this is a 2*2*2, or 23, factorial design. This design will have =8 different experimental conditions.

The notation used to denote factorial experiments conveys a lot of information. When a design is denoted by a 23 factorial, this identifies the number of factors (3); how many levels each factor has (2); and how many experimental conditions there are in the design (23 = 8).

Similarly, a 25 design has five factors with three levels, and 25 = 32) experimental conditions; and a 32 design has two factors, each with three levels, and (35 = 32) experimental conditions; and a degree has two factors each with a different number of levels. A 23 design has five factors-four with two levels and one with three levels and has 16×3=48 experimental conditions.

If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.