Principles of Experimental Designs in Statistics – Replication, Randomization & Local Control

What is a statistical experiment?

Ø  An experiment is a plan for the collection and analysis of data.
Ø  “It is a controlled act through which data are collected according to some pre-determined objective”.
Ø The observations obtained from a carefully planned and well-designed experiment in advance only gives valid inferences.
Ø An experimental design which gives the smallest error is supposed to be the best design for a particular type of investigation.

Experimental unit (Experimental Plot):

Ø  The smallest division of the experimental material to which we apply the treatment and can make the observation on it is called experimental unit or experimental plot

Treatments:

Ø  Treatments are the characteristics which are to be investigated through an experiment.

Ø  The treatments are the objects of comparisons in an experiment.

Ø  Example: effects of different fertilizers, the yield of different varieties of a crop, disease resistance of different cultivars etc

Things to remember when designing a Statistical Experiment

Ø  Select the right type of experimental design.

Ø  Should have an adequate number of replications.

Ø  Treatments should be randomly allocated to the experimental units.

Ø  Try to reduce extraneous factors as possible.

Ø  If possible, use the ‘local-control’ to reduce extraneous factors.

Design of Experiments in Agriculture

Ø  In agricultural experiments, an examiner has to divide the whole experimental unit or field into relatively homogenous sub-groups or strata.

Ø  These strata are called the blocks.

Ø  Each such block may contain many plots.

Ø  The land on which the trials is to be carried out is divided into as many blocks of the same size and shape and each of the blocks into as many plots of the same size and shape.

Ø  There will be ‘r’ blocks and ‘t’ plots, thus ‘rt’ plots together.

Ø  Experiments are allocated to the ‘t’  plots in the block.

Ø  The selection of the plot is random. For the random selection, we can use either lot method or random number table method.

Ø  Try to reduce the extraneous factors in the selection of plots.

What are Experimental Errors?

Ø  The variation in responses (results) caused by the extraneous factors is termed as experimental errors.

Ø  The experimental errors may arise due to:

$  The inherent variability in the experimental material to which the treatments are applied.

$  The lack of uniformity in the methodology of conducting the experiment.

$  Lack of representatives of the sample to the population under study.

Principles of Experimental Design

Ø  Professor Ronald A. Fisher pioneered the design of experiments in statistics.

Ø  In his classic book entitled ‘The Design of Experiments’ deals with many statistical experimental designs and its applications.

Ø  According to Fisher, a good experimental design should:

   (A).   Increase the efficiency of design

   (B).   Reduce the experimental errors

Ø  The increased efficiency and reduced experimental errors in experimental designs are achieved by THREE basic principles.

Ø  They are classically called the ‘Principles of Experimental Design’, they are:

(1).      Replication

(2).      Randomization

(3).      Local-control

(1). Replication

Ø  The repetition of the treatments under the investigation is called replication.

Ø  Single treatment does not produce variations in the results.

Ø  Replication of treatments increases the reliability of the estimates.

Ø  It helps to reduce the experimental errors.

Ø  However, replication alone has a limited role in increasing the efficiency of the design.

(2). Randomization

Ø  When all the treatments have an equal chance of being allocated to different experimental units is called randomization.

Ø  Randomization helps to eliminate the bias of any form.

Ø  In the absence of ‘replication’, the randomization will NOT be effective.

Ø  Replication and Randomization together form the foundation stone in the success of an experimental design.

(3). Local-control

Ø  The process of reducing the experimental errors by providing the relatively heterogeneous experimental areas into homogenous units is called Local-control.

Ø  The local-control will increase the efficiency of the experimental designs.

Ø  Local-control can be used to reduce the extraneous errors.

Ø  Reduction of extraneous errors reduced ‘experimental errors’.

Different types of Experimental Designs

Ø  Experimental designs are broadly classified into TWO categories:

(I).   Single-Factor Experiments

(II).  Multi-factor Experiments

(I). Single-Factor Experiments:

Ø  Single factor experiments are those experiments in which only a single factor varies while all others are kept constant.

Ø  Here the treatments consist exclusively of the different levels of the single variable factor.

Ø  All other factors are applied uniformly to all plots.

Ø  Examples of Single-Factor Experimental Designs:

(1)     Completely Randomized Design (CRD)

(2)     Randomized Block Design (RBD)

(3)     Latin-Square Design (LSD)

(II). Multi-Factor Experiments

Ø  Multi-factor experiments are also called as factorial experiments.

Ø  They are used in the experiments where the effects of more than one factor are to be determined.

Ø  A multi-factor experimental design is used to study a problem that is affected by a large number of factors.

References

Balaji, K. et al. (2012). Biostatistics. I.K. International Publishing House Pvt. Ltd., New Delhi

Kothari, C. R. (2004). Research Methodology: Methods and Techniques. New Age International.

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