17 ANNOVA-Narg

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ANOVA AND THE DESIGN OF

EXPERIMENTS


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THE MOST POPULAR RESEARCH METHOD.

THE OTHER CLASS OF STUDY IS KNOWN AS EXPERIMENTATION.

JUST LIKE IN A LABORATORY, HERE WE MANIPULATE CERTAIN

VARIABLES (USUALLY MARKETING MIX - PRICE, PROMOTION SHELF

SPACE, COLOUR OF PACKAGING ETC)

WE WOULD WANT TO KNOW ITS EFFECT ON OTHER VARIABLES (LIKE

SALES, OR CONSUMER PREFERENCES, BEHAVIOUR OR ATTITUDE)

AN EXPERIMENT CAN BE DONE WITH ONLY ONE INDEPENDENT

VARIABLE (FACTOR) OR WITH MULTIPLE INDEPENDENT VARIABLES.

INTRODUCTION AND APPLICATIONS


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METHODS

1. ANALYSIS OF VARIANCE - FOR STUDYING CAUSE-AND-EFFECT OF ONE OR

MORE FACTORS ON A SINGLE DEPENDENT VARIABLE.

A ONEINDEPENDENT VARIABLE EXPERIMENT IS CALLED ONE-WAY ANOVA.

2. IF WE HYPOTHESISE THAT THERE IS ALSO A BLOCKING VARIABLE IN ADDITION

TO ONE INDEPENDENT VARIABLE, WE CAN USE A RANDOMIZED BLOCK DESIGN.

3. FACTORIAL EXPERIMENT

WHEN MORE THAN ONE FACTORS (INDEPENDENT VARIABLES) ARE STUDIED.

ALSO FACILITATE THE STUDY OF POSSIBLE INTERACTION EFFECTS AMONG THE

INDEPENDENT VARIABLES.

4. MULTIVARIATE ANALYSIS OF VARIANCE- MANOVA

WHEN MORE THAN ONE DEPENDENT VARIABLES ARE STUDIED

WE WILL LIMIT OURSELVES TO FIRST THREE MAJOR TYPES OF ANOVA .


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VARIABLES

THE INDEPENDENT VARIABLES ARE OF NOMINAL SCALE (CATEGORICAL)

THE DEPENDENT VARIABLE IS METRIC (CONTINUOUS).

DESIGN

FOUR MAJOR TYPES OF DESIGNS,THREE FREQUENTLY USED TYPES WILL BE ILLUSTRATED WITH A WORKED OUT

EXAMPLE EACH.

THE FOUR MAJOR TYPES ARE

COMPLETELY RANDOMISED DESIGN IN A ONE-WAY ANOVA (SINGLE FACTOR)

RANDOMISED BLOCK DESIGN (SINGLE BLOCKING FACTOR)LATIN SQUARE DESIGN (TWO BLOCKING FACTORS)

FACTORIAL DESIGN WITH 2 OR MORE FACTORS.

WE WILL DISCUSS IN DETAIL THE FIRST TWO, AND THE FOURTH.


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ONE-WAY ANOVA

THERE IS ONLY ONE CATEGORICAL INDEPENDENT VARIABLE, AND ONE

DEPENDENT (METRIC) VARIABLE.

THE CAUSE

EACH CATEGORY OF AN INDEPENDENT VARIABLE IS CALLED A LEVEL.

MAY BE DIFFERENT LEVELS OF PRICES, OR DIFFERENT PACK SIZES, OR

DIFFERENT PRODUCT COLOURS.

THE EFFECT (DEPENDENT VARIABLE) COULD BE SALES, PREFERENCES

OR ATTITUDES TOWARDS THE BRAND.

IN THE EXAMPLE, WE WILL LOOK AT ADVERTISING COPY (INDEPENDENT

VARIABLE) PREFERENCE RATING FOR THE ADVERTISING COPY ( DEPENDENT

VARIABLE).


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WORKED EXAMPLE :

Three Different Versions Of Advertising Copy Are Created By An Advertising

Agency For A Campaign.

Adcopy 1, 2 And 3.

Before They Launch The Campaign, The Ad Agency Wants To Test Which Of The

Advertising Copy Is Preferred By Its Target Population.

A Sample Of 18 Respondents Is Selected From The Target Population.

At Random, These 18 Respondents Are Assigned To The 3 Versions Of Ad Copy.

Each Version Of Ad Copy Is Thus Shown To Six Of The Respondents.

The Respondents Are Asked To Rate Their Liking For The Ad Copy On A Scale Of 1

To 10. (1 = Not Liked At All, 10 = Liked A Lot ).


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INPUT DATA

INPUT DATA FOR THE 18 RESPONDENTS.

Fig. 1.

Sr.

No.

Ad

copy

rating

1 1 6.002 1 7.00

3 1 5.00

4 1 8.00

5 1 8.00

6 1 8.00

7 2 4.00

8 2 4.00

9 2 5.00

10 2 7.00


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Fig. 1. Contd

Sr.

No.

Ad

copy

rating

11 2 7.00

12 2 6.00

13 3 5.00

14 3 5.00

15 3 4.00

16 3 7.0017 3 8.00

18 3 7.00

PLEASE NOTE, THAT THESE EIGHTEEN RESPONDENTS

WERE RANDOMLY ASSIGNED TO EACH OF THE THREE AD VERSIONS. THIS RANDOM ASSIGNMENT IS CALLED

A COMPLETELY RANDOMISED ASSIGNMENT OR DESIGN.


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Fig. 2

Source of

Variation

Sum of

Squares

DF Mean

Square

F Sig.

of F

MainEffects

7.000 2 3.500 1.780 .203

ADCOPY 7.000 2 3.500 1.780 .203

Explained 7.000 2 3.500 1.780 .203

Residual 29.500 15 1.967

Total 36.500 17 2.147

OUTPUT

THE OUTPUT OF THE COMPUTERISED ONE-WAY ANNOVA

NULL HYPOTHESIS - THERE IS NO SIGNIFICANT DIFFERENCE IN THE MEAN RATINGS, H0: M1 = M2 = M3

WE HAVE ACCEPTED THE NULL HYPOTHESIS AT THE 95 PERCENT CONFIDENCE LEVEL

THE RATINGS GIVEN TO THE THREE AD COPY VERSIONS ARE NOT SIGNIFICANTLY DIFFERENT

FROM EACH OTHER CORRESPONDING TO SIGNIFICANCE LEVEL OF 0.05 (CONFIDENCE LEVEL

OF 95 PERCENT ).


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If We Had Simply Looked At The Mean Ratings For Each Ad Copy.

The Mean Rating Of Ad Copy Version-1 Is (6+7+5+8+8+8) / 6, Or 42/6 = 7.

Similarly, The Mean Rating Of Ad Copy Version-2 Is (4+4+5+7+7+6) / 6, Or 33/6 = 5.5.

The Mean Rating For Ad Copy Version-3 Is (5+5+4+7+8+7) / 6, Or 36/6 = 6.

The Three Mean Ratings Appear To Be Different 7, 5.5 And 6.

But The Anova Tells Us That This Difference Is Not Statistically Significant At The 95 PercentConfidence Level.

The Null Hypothesis For This F-test Is That There Is No Significant Difference In The Mean

Ratings For The Three Ad Copy Versions.

H0: M1 = M2 = M3

Thus, We Have Accepted The Null Hypothesis At The 95 Percent Confidence Level

(Or Failed To Reject The Null Hypothesis)

If The Significance Of F Had Been Less Than 0.05, We Would Have Rejected The Null

Hypothesis.

In That Case, We Would Have Concluded That Significant Differences Exist Between Mean

Ratings Given To The Three Ad Copy Versions.


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Three Versions Of The Adcopy Were Each Used In 6 Different Magazines. Magazines Are Coded 1,

2, 3, 4, 5, 6

Out Of The People Who Saw These Ads, 18 Randomly Chosen Respondents Are Picked, One

From Each Magazine.

In Other Words, We Have One Respondent For Every Combination Of Magazine & Adcopy

Hypothesis

The Magazine In Which The Version Of Adcopy Appears May Have An Impact On The Ratings

We Can Test This Hypothesis - By Doing An Anova With A Randomised Block Design. We Use The Variable Rating As The Dependent Variable, And Adcopy As The Factor, And

Magazine As The Block.

A Block Is Defined As Some Variable Which Could Affect The Relationship Between The

Independent Factor And The Dependent Variable.

We Are Trying To Remove The Effect Of The Magazine Used, By "Blocking" Its Effect. If We Do Not Block On A Variable, Its Effect Gets Included With The Error (Residual). This May Lead

To Wrong Conclusions About The Relationship Between The Independent And Dependent

Variables.


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Source ofVariation

SS DF MS F Sigof F

Residual 3.67 10 .37Adcopy 7.00 2 3.50 9.55 .005

Magazine 25.83 5 5.17 14.09 .000

(Total) 36.50 17 2.15

The first null hypothesis is that mean rating of the ADCOPY is the same for all 3 versions.

The second null hypothesis is that the block used (Magazine) has no effect on mean ratings

given to ADCOPY.

we want to test these hypotheses at the 95 percent confidence level.

We know that the significance level F in the last column should be less than 0.05

for the null hypothesis to be rejected.both the null hypotheses are rejected.

We conclude that the mean ratings given to the 3 versions of ADCOPY are

significantly different.

the MAGAZINE in which the ADCOPY appears has an impact on its rating.


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LATIN SQUARE DESIGN

THE LATIN SQUARE DESIGN IS AN EXTENSION OF THE RANDOMISED

BLOCK DESIGN. IT CONSISTS OF ONE INDEPENDENT VARIABLE

(FACTOR) AND TWO BLOCKS, INSTEAD OF ONE.

FACTORIAL DESIGNS

THIS TYPE OF DESIGN IS EMPLOYED WHEN WE HAVE 2 OR MORE

INDEPENDENT VARIABLES OR FACTORS.

THE MAJOR ADVANTAGE OF THIS DESIGN IS THAT MULTIPLE FACTORS

CAN BE SIMULTANEOUSLY TESTED.

THERE ARE TWO KINDS OF EFFECTS THAT WE CAN TEST.

MAIN EFFECT & INTERACTION EFFECT.


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WORKED EXAMPLE

We Are Testing The Effect Of Two Factors For A Toilet Soap Brand, Pack Design And

Price (Independent Variables) On

Sales (Dependent Variable).

We Would Like To Know

(1) If Each Of The Two Factors Independently Affects Sales ( The Main Effects)

(2) If There Is A Combined Effect Of Pack Design And Price ( The 2 Way Interaction

Effect) On Sales.

There Are 3 Levels Of Price Rs. 8, Rs. 11 And Rs. 14

There Are 3 Levels Of Pack Design Blue, Red And Green.

THE CODING OF THESE VARIABLES IS 1, 2, 3


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sr. no. sales Pack desn. price

1 500 1 1

2 440 2 1

3 360 3 1

4 300 1 2

5 280 2 2

6 250 3 2

7 200 1 3

8 150 2 39 250 3 3

10 600 1 1

11 450 2 1

12 510 3 1

13 400 1 2

14 350 2 215 300 3 2

16 250 1 3

17 275 2 3

18 220 3 3


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ANALYSIS

In This Case, We Are Testing Three Hypotheses.

Main Effects (2) :H0 : The Mean Level Of Sales Remains The Same For All 3 Levels Of Price.

Interaction Effect

H0 :The Mean Level Of Sales Remains The Same For All Combinations Of Pack

Design And Price.

We Found That Only The Price Effect Is Significant Statistically.

Thus, We Conclude That Price Alone Has An Impact On Sales.

Neither Pack Design Alone Nor The Combination Of Pack

Design With Price Have Any Significant Impact On Sales Of

The Toilet Soap.

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17 ANNOVA-Narg