Read this article to learn about:- 1. Planning of Experiments 2. Definition of the Design of Experiment 3. Basic Principles.
Planning of Experiments:
Experiments are carried out in order to test the validity of a hypothesis or to estimate the magnitude of an effect. But it is the common characteristic of experiments that when they are repeated the effects of experimental treatments, vary from trial to trial. Even after a number of repetitions, or replications, as they are called, the investigator still does not know by how much his results would be changed if the experiments were repeated further under the same condition.
If experiments are not planned properly, it may happen that no inference can be made or those which have been made may not answer the question to which the experimenter had hoped. Therefore, it is very essential to make a written draft of the proposals for any experiment.
This draft should have three parts:
(i) A statement of the objectives,
(ii) A description of the experiment,
(iii) An outline of the method of analysis of the results.
(i) A Statement of the Objectives:
The objectives should be specifically mentioned. They should clearly give the hypothesis which are to be tested or the effects which are to be estimated. They should clearly give the points which are to be given priority.
(ii) A Description of the Experiment:
The description should clearly mention the type of experimental material, thy size of the experiment, the number of replication or the experimental treatment. By experimental treatment we mean the different procedures whose effects are to be measured and compared e.g., manures, cultivation practices and methods of seed treatments.
(iii) The Method of Analysis of the Results:
Finally the draft should give the method or methods for drawing conclusions from the results. It may include a sketch of the analysis of variance.
Definition of the Design of Experiment:
Design of experiment is a logical construction of the experiment having a complete sequence of steps taken ahead of time to ensure that the appropriate data will be obtained in a way which permits an objective analysis of a particular problem leading to valid and precise inferences in most economic and useful forms.
Valid in the sense that conclusion drawn from it should be logically tenable and must be fret: from personal biases or preferences of the investigator. Precise in the sense that the random and non-random errors affecting the design should be controlled at a low level, so that every treatment can produces its effect under comparable and desired conditions.
Some Important Terms:
The important terms which are frequently used in the subject of ‘design of experiments’ are described in terms of agricultural experiments; but the same terms are also used in various other situations.
The different procedures or objects under comparison in an experiment are called treatments. For example, in a medical experiment the different drugs are treated.
(ii) Experimental Unit or Plot:
By experimental unit we mean the “object to which a treatment is applied in a single trial of the experiment and on which the variable under study is measured and analysed, The unit may be plot of land, a patient in a hospital or a batch of seeds or a group of pigs in pen.
(iii) Experimental Material or Field:
The set or group of experimental units is referred to as experimental material. However, experimental unit is the basic unit of the experimental material.
(iv) Blocking and Block:
The grouping of the experimental material in such a manner that units within a group are more like than are units in different groups is called blocking. The groups so obtained are known as blocks.
(v) Yield of Observations:
The measurements taken over treatments in experimental units are called observations or yield.
(vi) Experimental Error:
It is a characteristic of the experimental units that they produce different results all repeating any experiment. Some of the differences or variations are systematic and may be detected but some are apparently random and cannot be explained. These unexplained variations are termed as experimental error.
Basic Principles of Field Experimentation:
Fisher has given three basic principles for a good experimental design:
(1) Local control,
(1) Local Control (Blocking):
It aims at having blocks of comparatively homogeneous soil fertility. It is a device by which ‘error variance’ is minimized. It aims at minimizing the effects of chance causes.
The minimization of experimental error can be achieved by making use of the fact observed than adjacent areas in a field are relatively more homogeneous than those widely separated. Suppose the land is such that the fertility increase in the horizontal direction then the blocks should be taken perpendicular to the fertility trend so that each treatment gets equal advantage of fertility of land in different blocks.
The repetition of the treatments under investigation is known as replication. The replication of the experiment decreases the error associated with the difference between the average results for two treatments. If s2 is the error variance per unit and there are r replications, the error variance of the difference between the means two treatments is 2s2/r, and the corresponding standard error is s (√2/r).
On this basis we can calculate the number of replication required to enable us to infer the difference between two treatments, as significant at a particular level when observed difference exceeds a given mean. Replication is the only means of comparing ‘errors’. If the number of replication is increased, the accuracy of comparison increases, for example if r increases t increases when,
How many replications are required when an observed difference of 10% of the mean will be regarded as significant at 5% level; given that the true standard error per unit is 12% of the mean of the experiment and further given that I = 1.96 for being significant at 5% level a/significance.
Therefore, r should be 12; hence, minimum number of replication required is 12.
The allocation of treatments to various plots (experimental units) at random is called randomization. A set of treatments applied to a set of experimental units is said to the randomized when the treatment applied to any unit is chosen at random; Randomization helps in the objective comparison between treatments since the validity of the test of significance as the analysis of variance is based on the assumption of the randomness uses of the observations. Randomization is done with the help of random number tables.
Completely Randomized Design (CRD):
The simplest type of layout is that in which treatments are allotted to the units entirely by chance. If the treatment is to be applied to four units the randomization gives every group of four units in the experimental material an equal chance of receiving the treatment.
Randomization procedure is done with the help of the random number table by following steps are:
(1) Open the page of the table randomly.
(2) Select the columns of numbers on that page randomly.
(3) Numbers in that column will be used in order to determine the order of the rows the columns to be chosen.
(4) Extra numbers will be omitted.
The following table gives a layout of 4 treatments (t1, t2, t3, t4) each replicated times. The numbers in the bracket are the serial number of the experimental unit or plots:
Notation and Statistical Analysis:
To analyse the data obtained in it CRD, the observations are arranged according to treatments in the form of one-way classification. Then the notation and analysis of variance techniques used are similar to that one-way classification.
(Advantages and Disadvantages):
This design has the following advantages:
(1) Complete flexibility is allowed. The number of replications can be, varied at will from treatment to treatment. All the available, experimental material can be utilized.
(2) In this design any number of treatments and replications may be used.
(3) Even if the numbers of replications are not the same for all treatments, the statistical analysis is easy.
(4) The method of analysis remains simple when the results from some units or from whole treatments are missing or are rejected. Moreover, the relative loss of information due to missing data is smaller than with other design.
This design has the following disadvantages:
(1) The main disadvantage of the CRD is that the principle of local control is not used.
(2) If the experimental material is not homogeneous, the variation along the units enters into experimental error.
(3) The one and the main objection in this design are on the grounds of accuracy. Since there is no restriction on the randomization of the treatments we cannot be sure about the fact that the units receiving one treatment are similar to those receiving the other treatment, and therefore, the whole of the variation among the units enters into the experimental error.
Application of Completely Randomized Design:
The complete randomization is appropriate under the following circumstances:
(1) Where the experimental material is homogeneous and is limited in quantity.
(2) Where an appreciable fraction of the units is likely to be destroyed.
(3) Where in small experiments the increase accuracy from alternative designs does not outweigh the loss error degrees of freedom.
(4) The design is especially useful in small experiments where the supply of experimental material is scarce homogeneous, as whole of the materials utilized in the experiment.
Three treatments A, B, and C are composed in a completely randomized design with four replication of each. The layout and the yield in quintals per acre are given in the following table:
Analyse the experimental and state your conclusions.
First of all arrange the data in the following (one-way classification) form:
These results and the remaining calculations necessary to arrive at the required F value are shown in following analysis of variance table:
Since calculated value of F is less than table value of F at 5% level of significance for 2 and 9 degrees of freedom. Hence, Ho is accepted. That is mean yields of three varieties may be regarded equal.