Course Code: MAS 308

 

Topic 1: INTRODUCTION & DEFINITION OF TERMS.

In this topic, we introduce the concept of Design and Analysis of Experiments. Students will have the opportunity to learn key concepts associated with designing and analyzing Experiments.

 

By the end of this topic, learners should be able to:

1.      Explain the meaning of key concepts associated with the Design & Analysis of Experiments.

2.      Describe the procedure of experimentation.

3.      State and explain the principles of Experimentation

4.      Explain the efficiency of an experimental Design

5.      Explain the Concept of ANOVA.

Students to take note of the activities and exercises provided within the text and at the end of the topic.

 Topic Resources  

  Students to take note of the reference textbooks provided in the course outline.

v  Learners to get e-learning materials from the MMUST library and other links within their reach.

1.0 INTRODUCTION & DEFINITION OF TERMS. 1.1 INTRODUCTION

Design and analysis of experiments are concerned with

a)      Planning of an experiment

b)      Making relevant observations from the experiment

c)      Analyzing the results of the experiment.

An experiment is a procedure followed to obtain answers to a problem from a set of formulated questions.

There are two types of experiments namely absolute and comparative.

Design and analysis of experiments deals with comparative experiments while sample surveys deal with absolute problems.

In a comparative problem, a decision has to be made.

The decision is based on the observations made from experiments. Therefore for a good and reliable decision, the observations must be correct.

Every experiment involves a series of activities namely:

1.      Conjecture- The original hypothesis that motivated the experiment.

2.      Experiment- The test performed to investigate the conjecture.

3.      Analysis- The statistical treatment of data from the experiment so that it acquires meaning.

4.      Conclusion- Inferences/deductions from the experiments. The experiment will often lead to a revised conjecture, and new experiment, and so forth.

When designing an experiment to solve a particular comparative problem, the design should be done in such a way as to minimize errors.

 

Important terms

 

a)      Experimental unit- A physical entity that can be assigned at random to a treatment. A unit of statistical analysis. Suppose we intend to try out a set of fertilizers on a large farm. The farm needs to be divided into small convenient units on which the experiment can be performed. These units are called experimental units.

b)      Treatment – various objects of comparison in a comparative experiment. They include varieties of fertilizers, seed varieties, different methods of cultivation, etc.

c)      Blocks and plots. An experimental unit can be divided further into smaller units called blocks which can be further sub-divided into plots. see the illustration below:

Experimental unit

 

	PLOTS
B L O C K S
		,,	,,	,,	,,	,,
		,,	,,	,,	,,	,,
		,,	,,	,,	,,	,,

 

 

PRINCIPLES OF EXPERIMENTATION

According to R.A fisher, the basic principles of experimentation are:

a)      Replication – applying a treatment more than once. This is done in order to

i)                    Estimate experimental errors due to random variation and

ii)                    Reduce experimental errors of the mean yield.

b)      Randomization – The process of applying  treatments in such a way that each        treatment has the same chance of showing its effect. Randomization is important because

                                             i.            The estimated variance is only in the case of random sampling.

                                           ii.            Statistical tests can only be performed when randomness is assumed.

c)      Local control – Here all plots with similar characteristics are put together in one     block in such a way that a block is as homogeneous as possible but between blocks there is variation(heterogeneity). For instance plots with high fertility can be put together to form a block.

Homogeneous- Small variance

Heterogeneous – Large variance

 

 

EFFICIENCY OF A DESIGN

Efficiency of a design, D is defined by

Eff(D) =  , where  is then estimated mean effect.

Consider two designs and. We define the relative efficiency of    w.r.t  by

       

If, then is less efficient than and vice versa. (i.e.   is more efficient than).

 

ANALYSIS OF VARIANCE (ANOVA)

ü  ANOVA is a powerful tool for testing the significance of a given hypothesis.

ü  Suppose we are interested in testing whether the effects of four fertilizers are significantly different.

ü  The technique of ANOVA comes in handy.

ü  In every observation, there is an inherent variation which could be done to

                                 i.            Assignable causes or

                               ii.            Chance causes.

ü  The assignable causes can be traced and eliminated but chance causes cannot be eliminated. They are random in the nature and contribute to experimental error. They are beyond the experimenter’s control.

ü  In ANOVA we estimate the variation due to various causes and test their significance in order to establish the contributing components.