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Will higher trade discount

increase sale?

Will increase salary retain good

Salesmen in the company?

Will change in packaging

improve brand image?

Will outsourcing after sale

service improve customer

Satisfaction?

Questions

Testing cause-effectrelationship

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Terminology in causal designs

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Will higher trade discount increase sale?

Trade discount

Advertising exp.

Ability of salesman

Market potential

------------

Sale

INDEPENDENT VARIABLES

DEPENDENT

VARIABLE

Factor

Confounding

variables

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Factor : Trade discount

Current : 5%

5.5%

6.0%

6.5%

Factor levelsOr

Treatments

Stockists

Test Units

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Will higher trade discount increase sale?

Trade discount

Advertising exp.

Ability of salesman

Market potential

------------

Sale

INDEPENDENT VARIABLES

DEPENDENT

VARIABLE

Factor

Confounding

variables

Issue in assessing cause-effect relationship is:

How to control effect of confounding variables on dependent variable?

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Techniques to control effectof confounding variables

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Randomisation

Test units are assigned to treatments randomly

Effect of confounding variables on dependent variables isAveraged Easiest but least effective in controlling effect of confounding

variables

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Blocking

Blocks of test units are made based on confounding variables Test units from each block is selected in sample Treatments are assigned to test units by randomisation

FACTORTerritories(Blocks)

1% cash discount tostockist

1.5% cash discountto stockist

Urban

Rural

RandomisationRandomisationRandomisation

Randomisation

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Control Group

Two groups of test units are made by randomisation Treatment is given to only one group. Such a group is

called Experimental Group. Other group is calledControl Group

Data on Control Group gives effect of confounding variables

Data on Experimental Group gives effect of confoundingvariables& treatments

PLACEBO DRUG

Control Group Experimental Group

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Symbols in causal designs

We will use following symbols in studyingtypes of experimental designs:

X = Objects are exposed to treatment

O = Observation of dependent variable.Subscripts will be given to differentiate

observations (O1, O

2,)

R = Random assignment of treatments

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1. After-only without control

group This design is

XO1

Objects are exposed to treatment &observations are taken after exposure. For e.g.:

Cash discount 0f 2% is given to stockists & their

sales after discount are observed.

Suitable when standard of comparison isknown

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2. Before-After without Control

Group This design is

O1

X O2

This design offers comparison of sameobject before & after treatment

Treatment effect is (O2 O

1)

Assumed that effect of confoundingvariables before and after is same

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3. After only with One Control Group with

Randomization

Experimental Group R X O1

Control Group R O2

Treatment effect is (O1 O2)

Used when groups pre-treatment observationsare not possible or equal

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4. Before-After with One Control Group

Experimental group R O1 X O2

Control Group R O3 O4

Treatment effect is (O2 O1) (O4 O3) Allows for slightly unequal groups in terms

of confounding variables (i.e. O1 O3)

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Complex Designs

These are statistical designs

These designs are:

Completely Randomized Design (CRD) Randomized Block Design (RBD)

Factorial Design

Latin Square Design

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1. Completely Randomized

Design In this design, units are randomly assigned to

treatments

Factor is manipulated. For e.g.

Four training methods for training salesman are to betested. There are 40 salesmen in sample. These

salesmen are randomly assigned to training methods.

Their sales are then recorded. Here, training method

is factor. Four methods are treatments. Sale isdependent variable

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2. Randomized Block Design

This is a design in which effect of oneconfounding variable is controlled. Fore.g.:

In previous example, salesmans previous

experience might have impact on sale

In such case, groups (blocks) of no. ofyears of experience are made and

salesmen from each block are randomlyassigned to four methods. The design willlook as follows:

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2. Randomized Block Design

Treatm

Block

Method 1 Method 2 Method 3 Method 4

Less than 5years

6 to 10 years

More than 10years

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2. Randomized Block Design

By grouping salesmen into homogeneous

blocks, effect of one known confounding

variable i.e. experience is isolated

In this design, each block must receive

every treatment

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3. Factorial Design

In earlier two designs that we have seen

there was only one factor viz. Training

method

If we are interested to test the effects of

two or more factors, we use factorial

design

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3. Factorial Design

A Factorial design is denoted by levels of each

factor. For e.g.:

If there are 3 factors where factor 1 has two levels,

factor 2 has four levels & factor 3 has five levels, it isdenoted as 2x4x5

Effect of each factor on dependent variable is

called Main Effect

In addition to measuring main effect, Factorialdesign has advantage of measuring interaction

effect between two factors

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3. Factorial Design

There are two types of hypothesis viz.

Main effects on dependent variable are significant

Interaction effects on dependent variable are

significant

Treatm

Block

Method 1

(T1)

Method 2

(T2)

Method 3

(T3)

Method 4

(T4)

Less than 5 years 15.0 12.9 25.7 10.4

6 to 10 years 26.7 28.9 22.6 12.7

More than 10 years 10.6 14.5 25.1 11.2

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Latin Square Design

When we want to deal with two

confounding variables & one factor with no

interaction between two confounding

variables, we use Latin Square design

A Latin Square has equal no. of rows and

columns such that an alphabet appears

only once in a row & a column. For e.g.Latin square of order 3 will be as follows:

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Latin Square Design

1 2 3

I A B C

II B C A

III C A B

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Latin Square Design

Suppose, we feel that no. of years of

experience and academic discipline viz.

Arts, Science, Commerce of salesman are

two confounding variables in estimatingeffect of three methods of training on sale,

we will use Latin square design as follows:

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Latin Square Design

Arts Science

Commerce

Less than 5

years

T1 T2 T3

6 to 10years

T2 T3 T1

More than10 years

T3 T1 T2

1 2 3

I A B C

II B C A

III C A B

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Latin Square Design

Here, no. of levels of confounding

variables and factor should be same