🏜 Terms

Baics concepts of Experimental Designs

In order to verify a hypothesis pertaining to some scientific phenomena we have to collect data. Such data are obtained by either observation or by experimentation. The main topics connected with data collection are Theory of Sample Surveys and Experimental Designs.
In sample survey, a researcher makes observations on existing population and records data without interfering with the process that is being observed.
In experimentation, on the other hand, the researcher controls or manipulates the environment of the subjects that constitute the population.
The experiments allow a researcher to study the factors of his interest and show that these factors actually cause certain effects. Hence, whenever the objective is to study the effects of variables rather than simply to describe a population, we prefer the data collection through experimentation.
Modern concepts of experimental design are due primarily to R.A. Fisher. He developed them in the planning of agricultural field experiments. They are now used in many fields of science.

Basic concepts

In agricultural experiments, most of the times we divide the whole experimental unit (field) into relatively homogeneous sub-groups or strata.
These strata, which are more uniform amongst themselves than the field as a whole are known as blocks.

The objects of comparison in an experiment are defined as treatments.
For example:
- Suppose an Agronomist wishes to know the effect of different spacings on the yield of a crop, different spacings will be treatments. Each spacing will be called a treatment.
- If different fertilizer are tried in an experiment to test the responses of a crop to the fertilizer doses, the different fertilizers will be treatments and each dose will be a treatment.
- A teacher practices different teaching methods on different groups in his class to see which yields the best results.
- A doctor treats a patient with a skin condition with different creams to see which is most effective.

Experimental unit is the object to which treatment is applied to record the observations.
For example:
- In laboratory insects may be kept in groups of five or six. To each group, different insecticides will be applied to know the efficacy of the insecticides. In this study different groups of insects will be the experimental unit.
- If treatments are different varieties, then the objects to which treatments are applied to make observations will be different plot of land. The plots will be called experimental units.

The purpose of designing an experiment is to increase the precision of the experiment.
In order to increase the precision, we try to reduce the experimental error. For reducing the experimental error, we adopt some techniques. These techniques form the basic principles of experimental designs.
The basic principles of the experimental designs are replication, randomization and local control.

Repetition of treatment to different experimental units is known as Replication. In other words, the repetition of treatments under investigation is known as replication. We have no means of knowing about the variations in the results of a treatment. Only when we repeat the treatment several times we can estimate the experimental error.
A replication is used:
- To secure more accurate estimate of the experimental error, a term which represents the differences that would be observed if the same treatments were applied several times to the same experimental units
- To reduce the experimental error and thereby to increase precision, which is a measure of the variability of the experimental error.
- The standard error of treatment mean is σ/(√r). Where σ S.D. of treatment in the population and ‘r’ is is the number of replications. As ‘r’ increases, the standard error of mean decreases. Also in the analysis of variance the replication of treatments provides estimate of experimental error which is essential for the application of F-test.

When all the treatments have equal chances of being allocated to different experimental units it is known as randomization. or
Random allocation of treatments to different experimental units known as randomization.
The purpose of randomization is to remove bias and other sources of extraneous variation which are not controllable. Another advantage of randomization (accompanied by replication) is that it forms the basis of any valid statistical test. Hence the treatments must be assigned at random to the experimental units.
The purpose of randomization in field experiment is to control variance.
Randomization is usually done by using tables of random numbers.

It has been observed that all extraneous sources of variation are not removed by randomization and replication. This necessitates a refinement in the experimental technique. For this purpose, we make use of local control, a term referring to the grouping of homogeneous experimental units.
The main purpose of the principle of local control is to increase the efficiency of an experimental design by decreasing the experimental error.

The variation in the data due to uncontrolled factor is known as experimental error.

The shape and size of the blocks will usually depend up on the shape and size of the plots.
In order to control the experimental error it is desirable to divide the whole experimental area into different subgroups (blocks) such that within each block there is as much homogeneity as possible but between blocks there is maximum variation. Further each block is to be divided into as many plots as the number of treatments.
For maximum precision the plots should be rectangular in shape with their long sides parallel to the direction of the fertility gradient and the blocks should be arranged one after the other along the fertility gradient as shown in the figure.

👉🏻 A local structure of an experiment that helps in obtaining results with some precision.