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In this article we will discuss about:- 1. Meaning of Experimental Designs 2. **Principles of Experimental Designs 3. Factors.**

#### Meaning of Experimental Designs:

Experimental designs are various types of plot arrangements which are used to test a set of treatments to draw valid conclusions about a particular problem. Before dealing with experimental designs, it is necessary to define experiment, treatment and experimental unit.

A scientifically planned method is called an experiment and various objects of comparison are known as treatments. The group of material to which a treatment is applied in a single trial of experiment is known as experimental unit. It may a plot of land, a patient in a hospital, a group of cattle in a dairy, etc.

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**Experimental designs are useful to a researcher in several ways as given below:**

1. In reducing the soil heterogeneity and thereby experimental error to a considerable extent.

2. In testing the significance of difference among various objects of comparison.

3. In screening of various treatments in a scientific manner.

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4. In partitioning of variation into different components.

5. In the assessment of variances and co-variances.

6. In proper interpretation of scientific results and drawing valid conclusions.

**Principles of Experimental Designs:**

There are three basic principles of experimental designs, viz., replication, randomization and local control or error control. All these principles help in reducing the experimental error and thus make the experiment more efficient.

**These principles are briefly-described below: **

**1. Replication****:**

Repetition of treatments under investigation is known as replication.

**There are two main advantages of replications:**

i. Increase in replication increases the precision by reducing the error to a great extent. The increase in precision results in two ways. In case of field experiments standard error is calculated as VrVE / r where VE = error variance and r = number of replications. Thus, it is clear that the standard error of mean decreases as the number of replication increases.

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Increase in replication increases the degree of freedom of error which decreases the value of t due to decrease in confidence interval. The shortening of confidence interval is a good proof of increased precision.

ii. The error of experiment arises from the difference between the plots of the same treatment. Thus, without replications estimate of error is not possible and without the estimate of error comparisons are not possible.

Another way of reducing the experimental error is to increase the plot size. But the plot size cannot be increased beyond 0.1 acre, because further increase in plot will increase the heterogeneity within the plot and affect the advantage obtained by increasing the plot size.

As the smaller plots are homogeneous in fertility, it is better to keep the experimental area the same and increase the number of replications by shortening the plot size.

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**2. Randomization****:**

Allocation of treatments of different plots by a random process is known as randomization of treatments. Randomization gives equal chance to all the treatments for being allotted to a more fertile plot as well as to a less fertile plot.

**3. Local Control or Error Control****:**

The principle of making use of greater homogeneity in groups of experimental units for reducing the experimental error is known as local control.

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**The fertility of the field may be of two types: **

i. A major fertility variation which is usually marked by a fertility gradient.

ii. Sporadic or scattered fertility variations which are not systematic but are distributed in patches.

The first type of fertility effects are reduced by dividing the field into homogeneous blocks or replications and the effects of second type of fertility are minimized by randomization of treatments within the block. The experimental error should be reduced as far as possible because lower error helps in determining the small real differences between the treatments.

**Factors of Experimental Designs: **

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**The choice of experimental designs depends on three main factors, viz:**

(1) Number and nature of treatments under study,

(2) Objective of the experiment, and

(3) Available resources.

**Experimental Error****:**

The variation due to environmental factors or uncontrolled factors is called experimental error.

**Correction Factor****:**

If refers to the square of grand total divided by the number of observations. Thus, correction factor = (Grand total) 2/number of observations.

**Critical Difference****:**

The least significant difference, greater than which all the differences are significant is known as critical difference (CD).

Critical Difference = SE difference x t

S.E. difference = / r where VE = error variance, r = replications, t = table value at error degrees of freedom.

Critical difference is used to compare the observed differences among different treatments. If the difference is greater than critical difference, it is considered as significant and vice versa.

**F Test****:**

It is a test of significance which is used for testing the significance of differences among several treatments. It differs from z-test and t-test which are applied to test the significance of difference between two treatment means or between sample mean and population mean. For F test first we have to calculate F value.

**F Value****:**

It is the ratio between the treatment variance and error variance.

**It is also known as variance ratio and is estimated as given below: **

**F value = treatment variance/error variance****:**

The observed value of F is compared with the table value of F at appropriate degrees of freedom and at desired level of probability (5% or 1%). If the observed value of F is more than the table value, the differences among treatments are considered as significant and vice versa.