16497 mgt 252

Quantitative Technique is a scientific approach to managerial decision-making.

The successful use of Quantitative Technique for management would help the organization in solving complex problems on time, with greater accuracy and in the most economical way.

Suppose you watch a light flashing every 2 seconds, and another light flashing every 3 seconds, how would you calculate when the two lights would flash together?

BROAD CLASSIFICATION

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QUANTITATIVE TECHNIQUES

STATISTICAL TECHNIQUES

OPERATION RESEARCH (OR

PROGRAMMING) TECHNIQUES

STATISTICAL TECHNIQUESMethods of collecting DataClassification and tabulation of collected

dataProbability theory and sampling analysis.Correlation and Regression AnalysisIndex NumbersTime Series AnalysisRatio Analysis

OPERATION RESEARCH (OR PROGRAMMING) TECHNIQUESLinear Programming Decision TheoryTheory of GamesQueuing Theory

QT IN BUSINESS AND MANAGEMENTMANAGEMENT

i) Marketing: Selection of product mix, Sales resources allocation, analysis market research information, Sales forecastingii) Production Production planning, control and analysis Evaluation of machine performance Quality control requirements Inventory control measures

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QT IN BUSINESS AND MANAGEMENTiii) Finance, Accounting and Investment: financial forecast, budget preparation, Cash flow analysis, Capital budgeting, Dividend and Portfolio management, Financial planningiv) Personnel labour turnover rate employment trends performance appraisal wage rates and incentive plans

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ECONOMICS measure of GNP. determination of business cycle. comparison of market prices etc. analysis of population formulation of appropriate economic policies

RESEARCH AND DEVELOPMENT development of new product lines optimum use of resources evaluation of existing products

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QT IN BUSINESS AND MANAGEMENT

Understanding Research !Research

Literally, research (re-search) means “search again”.

Organized analysis of any subject based on “borrowed”

materials, with suitable acknowledgement.

A systematic, careful inquiry or examination to discover

new information about something, or establish new

relationships between things, and to expand and verify

existing knowledge for some specified purposes.

Objectives of ResearchTo find out answers to questions by

applying systematic and scientific techniques.

To obtain familiarity of any phenomenon.

To determine association between variables.

To determine characteristics of an individual or group of activities and frequency of occurrence.

Features of a Good ResearchObjectivityControlGeneralizationFree from personal biasSystematic (well planned research

design)ReproducibleRevealing of limitationsApplication of ethical standards

Ten Steps in the Marketing Research Process

1. Define the Problem2. Establish Research Objective3. Determine Research Design

4. Identify Information Needs and Sources5. Determine Methods of Data Collection6. Design Instrument for Data Collection7. Determine Sample Plan and Sample

Size8. Collect Data9. Analyze Data

10. Prepare and Present Final Report

Step 1: Define the research problem I The very first, and the most important step

in research:“A problem well-defined is half solved” Nature of the problem determines the type of

study to conduct. A research problem must be accurately and

precisely defined, otherwise the task of designing a good research difficult.

Step 1: Define the research problem II Get the right answer to the question:

“What exactly does the firm want (or need) to know?” The basic question to address is:

“How to know that there is a problem?” Problems may become apparent from:

deviation from the business plan, company records and reports, customer complaints and grievances, conversations with company employees, and observation of inappropriate behavior or conditions in the firm;

the success of the firm’s competitors, and published materials reporting issues such as, changes in market or environmental trends, new government regulations, anticipated changes in the economy, etc.)

Step 2: Establish Research Objectives

“If you do not know what you are looking for, you won’t find it”

Research objectives are related to and determined by the problem definition. In establishing research objectives, the researcher must answer the following questions:i) What specific information should the project provide? ii) If more than one type of information will be

developed from the study, which is the most important? and finally, iii) What are the priorities?

When specifying research objectives, development of hypotheses, might be very helpful.

When achieved, objectives provide the necessary information to solve the problem.

Step 3: Research Design

3. Research Design step involves the development of a research plan for carrying out the study. There are a number of alternative research

designs. The choice will largely depend on the research purpose.

EXPLO RATO RYF ocu s G rou p ;O b serva tion ;

O th ers .

Q UALITATIVE RESEARCH

DESCRIPTIVES u rvey research

CAUSALL ab ora to ry E xp erim en t

F ie ld E xp erim en t

Q UANTITATIVE RESEARCH

M ARKET ING RESEARCH

Step 4: Specify the information required. Step 5: Design the method of collecting the needed information.

4. After defining the problem the researcher must determine what kind of information will best meet the research objectives. Secondary

informationPrimary

information

5. Marketing research information may be collected in many ways: via mail, telephone, fax,

Internet, or personal interview.

using consumer panels, consisting of individuals.

Step 6: Design the questionnaire. A primary responsibilities of a marketing researcher

is to design the data collection instrument or questionnaire in a manner so that it is easily understood by the respondent and administered to them.

Step 7: Decide on the sampling design.

Step 8: Manage and implement the data collection. The researcher must determine the

criteria that would enable a respondent to take part in a study. The sampling design must result in the proper

sample of respondents being selected. Different sampling designs are available to researchers.

The researcher must properly manage and oversee the data collection process. If interview method is used, the researcher

must train interviewers and develop procedures for controlling the quality of the interviewing.

Step 9:Analyze and interpret the results. Step 10: Communicate the findings and implications.

The ‘raw’ research data needs to be edited, tabulated and analyzed to find the results and to interpret them. the method used may be manual or computer based. The analysis plan follows from the research objective of the

study. Association and relationships of variables are identified and

discussed in the light of the specific marketing problem.

The researcher has to submit a written report and often make an oral presentation to management or the client. In conducting all the marketing research activities; the

marketing researchers must adhere to ethical standards.

Correlation measures the strength of a relationship between two variables.

Correlation determines whether values of one variable are related to

another.

Independent and Dependent VariablesIndependent variable: is a variable that can

be controlled or manipulated.Dependent variable: is a variable that cannot

be controlled or manipulated. Its values are predicted from the independent variable.

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Example Independent variable

in this example is the number of hours studied.

The grade the student receives is a dependent variable.

The grade student receives depend upon the number of hours he or she will study.

Are these two variables related?

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Student Hours studied % Grade

A 6 82

B 2 63

C 1 57

D 5 88

E 3 68

F 2 75

Correlation CoefficientThe correlation coefficient computed from

the sample data measures the strength and direction of a relationship between two variables.

The range of the correlation coefficient is.- 1 to + 1 and is identified by r.

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Positive and Negative CorrelationsA positive relationship exists when both

variables increase or decrease at the same time. (Weight and height).

A negative relationship exist when one variable increases and the other variable decreases or vice versa. (Strength and age).

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Positive Correlation

0 < R < 1

No Correlation

R = 0

Negative Correlation

-1 < R < 0

Range of correlation coefficientIn case of exact

positive linear relationship the value of r is +1.

In case of a strong positive linear relationship, the value of r will be close to + 1.

Correlation = +1

15

20

25

10 12 14 16 18 20

Independent variable

De

pe

nd

en

t va

ria

ble

29

Range of correlation coefficientIn case of exact

negative linear relationship the value of r is –1.

In case of a strong negative linear relationship, the value of r will be close to – 1.

Correlation = -1

15

20

25

10 12 14 16 18 20

Independent variable

De

pe

nd

en

t va

ria

ble

30

Range of correlation coefficient

In case of a weak relationship the value of r will be close to 0.

Correlation = 0

10

15

20

25

30

0 2 4 6 8 10 12

Independent variable

De

pe

nd

en

t va

ria

ble

31

Computational Formula for CorrelationBy substituting and rearranging, you obtain a

substantial (and not very transparent) formula for xyr

2 22 2xy

N XY X Yr

N X X N Y Y

Cigarettes (X) Lung Capacity (Y)

0 45

5 42

10 33

15 31

20 29

Computing a correlationCigarettes (X)

XY

Lung Capacity (Y)

0 0 0 2025 45

5 25 210 1764 42

10 100 330 1089 33

15 225 465 961 31

20 400 580 841 29

50 750 1585 6680 180

2X 2Y

Computing a Correlation

2 2

(5)(1585) (50)(180)

(5)(750) 50 (5)(6680) 180

7925 9000

(3750 2500)(33400 32400)

1075.9615

1250 (1000)

xyr

Example for correlation coefficientStudent Age Blood Pressure

A 43 128

B 48 120

C 56 135

D 61 143

E 67 141

F 70 152

Example for correlation coefficientUsing the

data on age and blood pressure, let’s calculate the x, y, xy, x2

and y2.

37

Student Age Blood Pressure

Age*BP

age2 BP2

A 43 128 5504 1849 16384

B 48 120 5760 2304 14400

C 56 135 7560 3136 18225

D 61 143 8723 3721 20449

E 67 141 9447 4489 19881

F 70 152 10640 4900 23104

Sum 345 819 47634 20399 112443

Example for correlation coefficientSubstitute in the formula and solve for r:

r= {(6*47634)-(345*819)}/{[(6*20399)-3452][(6*112443)-8192]}0.5.

r= 0.897.The correlation coefficient suggests a strong

positive relationship between age and blood pressure.

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The conceptual formula for the correlation coefficient is a little daunting, but it looks like this:

Example for correlation coefficientShyness

XSpeeches Y

0 8

2 10

3 4

6 6

9 1

10 3

Computational Example of r for the relationship between Shyness and Speeches

Shyness

XSpeeches Y

XY X2 Y2

0 8 0 0 64

2 10 20 4 100

3 4 12 9 16

6 6 36 36 36

9 1 9 81 1

10 3 30 100 9

30 32 107 230 226

(6 X 107) – 30 (32)

[6 (230) – 302] [6 (226) – 322 ]

r = -.797

Alternative Formula for the Correlation Coefficient

xyxy

x y

sr

s s

sxi x

n2

2

1

( )s

xi x

n2

2

1

( )

Partial correlationSometimes it is desirable to know the

relationship between two variables with the effects of a third variable held constant.

E.g: Both intelligence and number of hours worked are correlated with exam marks, and further that intelligence and number of hours worked are also correlated.

Partial correlationPartial correlation is the correlation of two

variables while controlling for a third or more other variables.

Partial correlation coefficient is a measure of the linear association between two variables after adjusting for the linear effect of a group of other variables.

Partial correlation analysis is important when studying relationship in linear form between more than two variables

It measures the strength of a linear relationship between two variables, while controlling the effect of other variables.

For example r12.34 is the correlation of variables 1 and 2, controlling for variables 3 and 4.

If partial correlation r12.34 is equal to uncontrolled correlation r12 , it implies that the control variables have no effect on the relationship between variables 1 and 2..

Types of Partial correlationIf the number of other variables is equal to 1,

the partial correlation coefficient is called the first order coefficient.

If the number of other variables is equal to 2, the partial correlation coefficient is called the second order coefficient, and so on.

Types of Partial correlation

ProblemsA. Calling exam marks (1), intelligence (2)

and hours worked (3), and given r12 = .50, and r13=.40, and r23 of .40

work out the value of r12.3.

Given three variables (1) prognosis in terms of weeks to recover, (2) an anxiety questionnaire, (3) a physiological measure, and r12= .40; r13= .30, and r23= .80, what is the correlation of the physiological measure with prognosis with the anxiety questionnaire results partialled out from both variables?

Partial correlation of (1) (actual sale price ÷ $1000) with (2) (living space), controlling for (3) (current taxes) and (4) (number of rooms)