Foundations of Experimental Design

Presented by

Dr.J.P.VermaMSc (Statistics), PhD, MA(Psychology), Masters(Computer Application)

Professor(Statistics)

Lakshmibai National Institute of Physical Education, Gwalior, India

(Deemed University)Email: vermajprakash@gmail.com

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Research Objectives

To test a theory through deductive logicTo develop a theory through inductive logic

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The exercise intensity with 65% maximum heart rate may

improve the cardio- respiratory endurance significantly.

How Theories are tested ?

By means of Hypothesis

Example

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If most of the sports persons are medal winners from a particular university their training programme may be superior than the other universities.

How theories are developed?

By observing a phenomenon

Example

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This Presentation is based on

Chapter 1 of the book

Repeated Measures Design for Empirical Researchers

Published by Wiley, USA

Complete Presentation can be accessed on

Companion Website

of the Book

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To investigate some kinds of relationship between

independent and dependent variables.

Purpose of Empirical Research?

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lack cause and effect relationships Reduced internal validity

Types of Empirical Research

Non Experimental or Correlational

Experimental Explain cause and effect

relationships Higher internal validity

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Why Experimental Research has more Validity?

Experimenter manipulates independent variable

to see its impact on dependent variable

by controlling extraneous factors

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What is Design of Experiment?

 Organizing a controlled experiment to generate data for understanding the

causes of variation

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 Principles of Design of Experiment

- Ensures homogeneity in the experimental groups- Enhances external and internal validity in the study

Randomization

Replication - Repeating an experiment a number of times on subjects/ experimental units

- A way of reducing experimental error by including an extraneous variable in the experiment.

- Heterogeneous experimental units are divided into homogenous blocks

- Treatments are randomly allocated in these blocks.

Blocking

Statistical Designs

Used when experimental material/subjects are homogeneous

Effect of one factor on dependent variable is investigated

Classification of Statistical Designs in Research

A. Completely Randomized Design(CRD)

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127

3

9 10

1 2

11 64

6 1 11Stage 1

2 9 4Stage 2

5 12 3Stage 3

7 8 10Stage 4

T2 T1 T3

T1 T3 T2

T2 T3 T1

T3 T1 T2

Sample

Comparing effect of three advertisements T1, T2 and T3 on sale of a product

Example

Figure 1.1 Layout of the completely randomized design

Fig.1.1 Layout of completely randomized design

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Statistical Designs …Cont

Used when experimental material/subjects are heterogeneous

Effect of one factor on dependent variable is investigated by introducing the blocking variable in experiment.

B. Randomized Block Design

T1 T3 T2Low IQ

Average IQ

High IQ

Blo

ck: I

Q

T3 T1 T2

T2 T3 T1Allocation of treatments in block

Block 1

Block 2

Block 3

Subjects in block

Fig.1.2 Layout of randomized block design

To study the effect of three different types of teaching methodologies T1, T2 and T3 on learning efficiency.

Example

 Statistical Designs …Cont

Special case of randomized block design Subjects are matched on some characteristics which

are supposed to affect the experimental variable Here each matched pair is like a block Only comparison of two treatments is possible

B(i). Matched Pairs Design

S1

S4

S5

S100

Subjects in each pair

Pair 1

Pair 2

Pair 3

Treatment

S2

S3

S6

S99

Exercise

Placebo

. . . . . .

Pair 50

Figure 1.3 Layout of matched pairs design

To study the effect of exercise on strength in 100 students

Example

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 Statistical Designs

C. Latin Square Design

In this design random variation of two factors is controlled Two blocking factor can be taken in this design Number of rows columns and treatments are required to be same

in this design. Each treatment can occur only once in the corresponding row and

column.

Low

Average

High Blo

ck: I

Q

Fig.1.2 Layout of Latin square design

To study the effect of three different types of teaching methodologies T1, T2 and T3 on learning efficiency.

Example

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T1 T2 T3T3 T1 T2T2 T3 T1

Block: Age

TeensMid age

Old age

Factorial Experiment Organized in CRD

 If factors A(exercise intensity) has three levels(low , medium and high) and B(Environment) also has three levels(hot, humid and cold) then nine treatment groups are required.

To investigate the effect of two or more factors on a dependent

variable simultaneously

ExampleLow

Medium

High

Hot Humid Cold

Cells

Subjects in each cell

Fact

or A

: Men

tal E

xerc

ise

Factor B: Environment

Figure 1.4 Layout of 3×3 factorial experiment in CRD 15

Dependent Variable: Task efficiency

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Terminologies in Design of Experiment

- Experimental unit on which experiment is conducted

Subject

Treatment - Levels of the independent variable whose effect is to be

seen on the dependent variable.

- A variable of interest

- An independent variable whose effect is to be seen on the dependent variable

Criterion Variable

Factor

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Explanation of Terms

To see the effect of

Aerobic exercise with different intensity

on the

Cardio respiratory endurance

in

Housewives

Subjects

Treatments: Intensities of aerobic exercise

Factor: Aerobic exercise

Criterion variable

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Terminologies in Design of Experiment

- Spread of ScoresVariation

- Measure of VariationVariance

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Terminologies in Design of Experiment

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43

1

16 3

14

1366

321

48

17

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How to measure variation?

Can be estimated by

Range

Variance

Q.D.

Mean Dev.

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Population vs Sample Variance

22 xN1

22 xx1n

1S

Population variance =

Mean Square Deviation

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43

1

16 3

14

1366

321

48

17

3213

Population

Sample

11

2 143

Whether the population variance can be estimated correctly by the sample variance ?

S2 is an unbiased estimate of population variance

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Terminologies in Design of Experiment

Uncontrolled error in an experiment Attributed to non-assignable causes Individual variation

Experimental Error

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Terminologies in Design of Experiment

Extent of generalizibility of findings to the population from which sample has been drawn.

External validity

Extent to which one can say that the variation observed in the Dependent variable(DV) is due to the variation in the Independent variable(IV).

Internal Validity

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Sum of SquaresVariation among scores

22 xx1n

1SMean Square Deviation =

dfVariation

dfSS

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Controlling Variance in Experimental Design

Purpose of Experimental DesignMaximize Systematic VarianceControl Extraneous VarianceMinimize Error Variance

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Controlling Variance in Experimental Design - An Example

Effect of 2 weeks Teaching methodology on performance

Traditional Method T1

Flexible method T3

Audio-visual Method T2

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98

77

54

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Systematic variance

High IQ

Low IQExtraneous variance: IQ

Error variance

Mixed IQ

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