research methodology ver5

8/8/2019 Research Methodology Ver5

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Chapter 1

Management research:

It is the systematic and objective identification, collection, analysis,

dissemination and use of information for the purpose of improving

decision making related to the identification and solution of problems

and opportunities in management.

Research is done for two reasons 1) to identify management

problems, 2) to solve management problems.

Management research involves the identification, collection, analysis,dissemination, and use of information. It is a systematic and objective

process designed to identify and solve management problems. Thus

management research can be classified as problem identification

research and problem solving research.

The management research process:It is a set of six steps that defines the task to be accomplished in

conducting a management research study.

These include problem definition, development of an approach to the

problem, research design formulation, field work, data preparation

and analysis, report preparation and presentation.

Problem identification research:

Research that is undertaken to help identify problems that are not

necessarily apparent on the surface and get exist or are likely to arise

in the future.


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Problem solving research:

Research undertaken to help solve specific management problems.

The management research process consists of six steps that must be

followed systematically. The role of management research is to

assess information needs and provide relevant information in order to

improve management decision making. However, the decision to

undertake management research is not an automatic one but must be

carefully considered.

Management research may be conducted internally or may be

purchased from external suppliers, referred to as the management

research industry. Full service suppliers provide the entire range of

management research services from problem definition to report

preparation and presentation. The services provided by these

suppliers can be classified as syndicated, standardized, customized,or internet services. Limited service suppliers specialize in one or a

few phases of the management research project. Services offered by

these suppliers can be classified as field services, coding, and data

entry, data analysis, analytical services, or branded products.

Competitive intelligence: the process of enhancing market place

competitiveness through a greater understanding of a firms

competitors and the competitive environment.

Due to the need for management research, attractive career

opportunities are available with management research firms,


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business and non-business firms, agencies with management

research departments, and advertising agencies. Information

obtained using management research becomes and integral part of

the MIS and DSS. Management research contributes to the DSS by

providing research data to the database, management models and

analytical techniques with model base, and specialized management

research programmes to the software base. International

management research is much more complex than domestic research

as the researcher must consider the environment prevailing in the

international markets that are being researched. The ethical issues in

the management research involve four stake holders.1. Management Researcher

2. The Client

3. The Respondents

4. The Public

The internet can be used at every step of the management researchprocess. SPSS windows is an integrative package that can greatly

facilitate management research.

Chapter 2

Defining the marketing research problem is the most important step

in a research project. It is a difficult step, because frequently

management has not determined the actual problem or has only a

vague notion about it. The researchers role is to help management

identify and isolate the problem.


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Problem definition: It is a broad statement of the general problem and

identification of the specific components of the marketing research

problems.

Problem Audit: A comprehensive examination of a marketing problem

to understand its origin and nature.

The tasks involved in formulating the marketing research problem

include discussions with management including the key decision

makers, interviews with industry experts, analysis of secondary data,

and qualitative research.

Secondary data: Data collected for some purpose other than the

problem at hand.

Primary data: Data originated by the researcher specifically address

the research problem.

Qualitative research: An unstructured, exploratory research

methodology based on small samples intended to provide insight and

understanding of the problem setting.

Pilot surveys: Surveys that tend to be less structured then large scale

surveys in that they generally contain more open ended questions

and the sample size is much smaller.


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marketing research problem is to make a broad statement of the

problem and then identify its specific components.

The Process of Defining the Problem and Developing an Approach

Tasks Involved

Discussions

with

Decision

Makers

Interview

with

Experts

Secondary

Data

Analysis

Qualitative

Research

Environmental Context of the Problem

Step 1: Problem Definition

Management Decision Problem

Marketing Research Problem

Approach to the Problem

Objective/

Theoretical

Foundations

Analytical

Model:

Verbal,

Graphical,Mathematical

Research

Questions

Hypothesis Specification

of InformationNeeded

Step 3: Research Design

Developing an approach to the problem is the second step in the

marketing research process. The components of an approach consist


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of an objective framework, analytical models, research questions,

hypothesis and specification of information needed. It is necessary

that approach developed be based on objective or empirical evidence

and be grounded in theory.

The steps needed for development of research questions and

hypothesis are:

1) Components of marketing research problem. Here we set

objective or theoretical framework.

2) Research questions are framed.

3) Analytical model is developed.4) Hypothesis is stated.

The relevant variables and their inter-relationships may be neatly

summarized and via an analytical model. The most common kinds of

model structures are verbal, graphical, and mathematical.

Analytical model: An explicit specification of a set of variables and

their interrelationships designed to represent some real system or

process in whole or in part. They can have three forms: 1) Verbal

models 2) Graphical models 3) Mathematical Models.

The research questions are refined statement of the specific

components of the problem that ask what specific information is

required with respect to the problem components. Research

questions may be further refined in to hypothesis. Finally given the

problem definition, research questions, and hypothesis the

information needed should be specific.


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Hypothesis: an unproven statement or proposition about a factor or a

phenomenon that is of interest to the researcher.

When defining the problem in international marketing research, the

researcher must isolate and examine the impact of the self reference

criterion (SRC), or the unconscious reference to ones own cultural

values. Several ethical issues that have an impact on the client and

the researcher can arise at this stage but can be resolved by adhering

to the seven Cs: Communication, Corporation, Confidence, Candor,Closeness, Continuity, and Creativity.

Chapter 3

A research design is a framework or blueprint for conducting the

marketing research project. It specifies the details of how the projectshould be conducted. Research designs may be broadly classified as

exploratory or conclusive.

Research design: a frame work or blue print for conducting the

marketing research projects. It specifies the details of the procedures

necessary for obtaining the information needed to structure and solve

marketing research problems.

Research designs could be classified as exploratory or conclusive.


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Exploratory research: One type of research design, which has as its

primary objective the provision of insights into and comprehension of

the problem situation confronting the researcher.

Conclusive Research: research designed to assist the decision maker

in determining, evaluating and selecting the best course of action to

take in a given situation. Conclusive research is typically more formal

and structured than exploratory research.

Research Design

ExploratoryResearch

Design

ConclusiveResearch

Design


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Classification of Marketing Research Designs

The primary purpose of exploratory research is to provide insights

into the problem. Conclusive research is to provide insights into the

problem. Conclusive research is conducted to test specific

hypotheses and examine specific relationships. The findings from

conclusive research are used as input into managerial decision

making. Conclusive research may be either descriptive or casual.

The major objective of descriptive research is to describe market

characteristics or functions. A descriptive design requires a clear

specification of the who, what, when, where, why, and way of the

research. Descriptive research can be further classified into cross-

CausalResearch

DescriptiveResearch

LongitudinalDesign

Cross-SectionalDesign

SingleCross-Sectional

Design

MultipleCross-Sectional

Design


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sectional designs involve the collection of information from a sample

of population elements at a single point in time. In contrast, in

longitudinal designs repeated measurements are taken on fixed

samples. Casual research is designed for the primary purpose of

obtaining evidence about cause and effect (casual) relationships.

Comparison of Basic research designs:

Traits Exploratory Descriptive CausalObjective Discover Ideas

and insights

Describe Market

characteristics or functions

Determine

cause and effectrelationships

Characteristics Flexible Marked by the

prior formulation

of specific

hypothesis

Manipulation of

one or more

independent

variablesVersatile Preplanned and

structured design

Control of other

mediatingvariables

Often the front

end of total

research

designMethods Expert surveys Secondary data

(analyzedquantitatively)

Experiments

Pilot surveys SurveysSecondary

data (analyzed

qualitatively)

Panels

Qualitative Observational


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research and other data

Descriptive Research: A type of conclusive research that has as its

major objective the description of something like marketcharacteristics or functions. A descriptive design requires a clear

specification of the who, what, when, where, why and way (the six

Ws).

Cross-Sectional Design: A type of research design involving the

collection of information from any given sample of populationelements only once.

Single Cross-sectional Design: A cross-sectional design in which one

sample of respondents is drawn from the target population and

information is obtained from this sample once.

Multiple Cross-sectional Designs: A cross-sectional design in which

there are two or more samples of respondents, and information from

each sample is obtained only once.

Cohort Analysis: A multiple cross-sectional design consisting of a

series of surveys conducted at appropriate time intervals. The cohort

refers to the group of respondents who experience the same eventwithin the same time interval.

Longitudinal Design: A type of research design involving a fixed

sample of population elements that is measured repeatedly on the


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same variables. The sample remains the same over time, thus

providing a series of pictures which, when viewed together, portray a

vivid illustrations of the situation and the changes that are taking

place over time.

Panel: A sample of respondents who have agreed to provide

information at specified intervals over an extended period.

Casual Research: A type of conclusive research where the major

objective is to obtain evidence regarding cause-and-effect

relationships.

A research design consists of six components. Error can be

associated with any of these components. The total error is

composed of random, sampling error and non-sampling error. Non-

sampling error consists of non-response and response errors.

Response errors encompass errors made by researcher, interviewers,and respondents. A written marketing research proposal including all

the elements of the marketing research process should be prepared.

In formulating a research design when conducting international

marketing research, considerable effort is required to ensure the

equivalence and comparability of secondary and primary data

obtained from different countries.

Total Error: The variation between the true mean value in the

population of the variable of interest and the observed mean value

obtained in the marketing research projects.


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Random Sampling Error: The error due to the particular sample

selected being an imperfect representation of the population of

interest. It may be defined as the variation between the true mean

value for the sample and the true mean value of the population.

Non-sampling Error: Non-sampling errors are errors that can be

attributed to sources other than sampling, and they can be random or

nonrandom. They result from a variety of reasons, including errors in

problem definition, approach, scales, questionnaire design,

interviewing methods, and data preparation and analysis. These

errors consist of non-response errors and response errors.

Non-response Error: A type of non-sampling error that occurs when

some of the respondents included in the sample do not respond. This

error may be defined as the variation between the true mean value of

the variable in the original sample and the true mean value in the net

sample.

Response Error: A type of non-sampling error arising from the

respondents who do respond, but give incorrect answers or their

answers are mis-recorded or mis-analyzed. It may be defined as the

variation between the true mean value of the variable in the net

sample and the observed mean value obtained in the marketing

research project. The Response errors are categorized in to three

categories:

1) Researcher Errors

2) Interviewer Errors

3) Respondent Errors


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Further Researcher Errors include following sub-classifications:

) Surrogate Information error : Variation between the information

needed for the research problem and the information sought by

the researcher. E.g. Consumer preferences are recorded instead

of consumer choice of a new brand.

) Measurement Error: Variation between the information sought

and the information generated by the measurement process

employed by the researcher. e.g. employing a scale that

measures perceptions rather than preferences.

c) Population definition error: Variation between the actualpopulation relevant to the problem at hand and the population

as defined by the researcher.

d) Sampling Frame Error: Variation between the population

defined by the researcher and the population as implied by the

sampling frame used. E.g. a list of telephone numbers from

directory does not represent population of potential consumersbecause of unlisted, disconnected and new numbers in service.

) Data Analysis Error: It occurs when an inappropriate statistical

procedure is used, resulting in incorrect interpretation and

findings.

Interviewer Errors include following sub-classifications:

a) Respondent Selection Error: It occurs when interviewers select

respondents other than those specified by the sampling design

or in a manner inconsistent with the sampling design.

b) Questioning Error: Errors made in asking questions to the

respondents or in not probing when more information is needed.


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E.g. interviewer does not use the exact wording given in the

questionnaire.

c) Recording Error: Errors in hearing, interpreting, and recording

the answers given by the respondents. E.g. interviewer thake a

neutral response as positive response.

d) Cheating Error: It arises when the interviewer fabricates answers

to a part or all of the interview.

Respondents Errors include following sub-classifications:

a) Inability Error: The respondents inability to provide accurate

answers due to fatigue, unfamiliarity, boredom, question format,content, or other factors.

b) Unwillingness Error: The respondents unwillingness to provide

accurate information because of a desire to provide socially

acceptable answers, avoid embarrassment, or please the

interviewer.

Marketing Research Proposal / Synopsis: The official layout of the

planned marketing research activity for management. It describes the

research problem, approach, the research design, data collection

methods, data analysis methods, and reporting methods. All steps of

the marketing research process contains the following elements:

1) Executive Summary

2) Background

3) Problem Definition / Objectives of the Research

4) Approach to the problem

5) Research Design

6) Field Work / Data Collection


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7) Data Analysis

8) Reporting

9) Cost & Time

10) Appendices

In terms of ethical issues, the researchers must ensure that the

research design utilized will provide the information sought, and that

the information sought is the information needed by the client. The

client should have the integrity not to mis-represent the project and

should describe the situation that the researcher must operate within

and not make unreasonable demands. Every precaution should betaken to ensure the respondents or subjects right to safety, right to

privacy, or right to choose.

Chapter 8

Measurement is the assignment of numbers or other symbols to

characteristics of objects according to set rules. Scaling involves the

generation of continuum upon which measured objects are located.

Measurement: The assignment of numbers or other symbols to

characteristics of objects according to certain pre-specified rules.


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Scaling: The generation of a continuum upon which measured objects

are located.

The four primary scales of measurement are nominal, ordinal,

interval, and ratio. Of these, the nominal scale is most basic in that

the numbers are used only for identifying or classifying objects.

Nominal Scale: A scale whose numbers serve only as labels or as

tags for identifying and classifying objects with a strict one to one

correspondence between the numbers and the objects.

Ordinal Scale: A ranking scale in which numbers are assigned to

objects to indicate the relative extent to which some characteristic is

possessed. Thus, it is possible to determine whether an object has

more or less of a characteristic than some other object.

Interval Scale: A scale in which the numbers are used to rate objects

such that numerically equal distances on the scale represent equal

distances in the characteristic being measured.

Ratio Scale: It is the highest scale. It allows the researcher to identify

or classify objects, rank order the objects, and compare intervals or

differences. It is also meaningful to conclude ratios of the scale

values.

In the ordinal scale, the next higher level scale, the numbers indicate

the relative position of the objects but not the magnitude of difference


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between them. The interval scale permits a comparison of the

difference between the objects. However, as it has an arbitrary zero

point, it is not meaningful to calculate ratios of scale values on an

interval scale. The highest level of measurement is represented by the

ratio scale in which the zero point is fixed. The researcher can

compute ratios of scale values using this scale. The ratio scale

incorporates all the properties of the low level scales.

Table 8.1

Scale Basic

Characteristics

Common

Examples

Marketing

Examples

Descriptiv

e

Inferential

Nomina

l

Numbers

Identify and

classify objects

Social

Security

Numbers,

numbering

of football

players

Brand

numbers,

store types,

Gender

classificatio

n

Percentage

s, Mode

Chi-square,

binomial

test

Ordinal Numbers

indicate the

relative

positions of the

objects but not

the magnitude

of differences

between them

Quality

Rankings,

rankings of

teams in a

tournament

Preference

rankings,

market

position,

social class

Percentile

Median

Rank-order

correlation,

Friedman

ANOVA

Interval Differences

between objects

can be

compared; zero

point is

arbitrary

Temperatur

e

(Fahrenheit

,

centigrade)

Attitudes,

opinions,

index

numbers

Range,

mean,

standard

deviation

Product

moment

correlation

s, t-tests,

ANOVA,

Regression


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, factor

analysisRatio Zero point is

fixed; ratios of

scale values

can be

computed

Length,

weight

Age,

income,

costs,

sales,

market

shares

Geometric

mean,

harmonic

mean

Coefficient

of variation

Scaling techniques can be classified as comparative or non

comparative. Comparative scaling involves a direct comparison of

stimulus objects. Comparative scales include paired comparisons,

rank order, constant sum, and the Q-sort. The data obtained by these

procedures have only ordinal properties.

Comparative Scales: One of the two types of scaling techniques in

which there is direct comparison of stimulus objects with oneanother.

Non-Comparative Scales: One of the two types of scaling techniques

in which each stimulus object is scaled independently of the other

objects in the stimulus set.

Scaling Techniques

Non-Comparative ScalesComparative Scales

Q-Sort & Other

Procedures

Rank

Order

Paired

Comparison

Constant

Sum


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Figure: Classification of Scaling Techniques

Paired Comparison Scaling: A comparative scaling technique inwhich a respondent is presented with two objects at a time and asked

to select one object in the pair according to some criterion. The data

obtained are ordinal in nature.

Transitivity of Preference: An assumption made in order to convert

paired comparison data to rank order data. It implies that if brand A ispreferred to brand B and brand B is preferred to Brand C, then the

brand A is preferred to brand C.

Rank Order Scaling: A comparative scaling technique in which

respondents are presented with several objects simultaneously and

asked to order or rank them according to some criteria.

Constant Sum Scaling: A comparative scaling technique in which

respondents are required to allocate a constant sum of units such as

points, dollars, chits, stickers, or chips among a set of stimulus

objects with respect to some criteria.

ContinuousRating Scales

ItemizedRating Scales

Likert SemanticDifferential

Stapel


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Q-Sort Scaling: A comparative scaling technique that uses a rank

order procedure to sort objects based on similarity with respect to

some criteria.

Respondents in developed countries, due to higher education and

consumer sophistication levels, are quite used to providing

responses in interval and ratio scales. However, in developing

countries, preferences can be best measured by using ordinal scales.

Ethical considerations require that the appropriate type of scale beused in order to get the data needed to answer the research

questions. And test the hypotheses. The Internet, as well as several

specialized computer programmes, are available to implement

different types of scales.

Chapter 9

In non-comparative scaling, each object is scaled independently of

the other objects in the stimulus set. The resulting data is generally

assumed to be interval or ratio scaled. Non-comparative rating scales

can be either continuous or itemized. The itemized rating scales are

further classified as Likert, semantic differential, or Stapel scales.

Then using non-comparative itemized rating scales, researcher must

decide on the number of scale categories, balanced versus

unbalanced scales, odd or even number of categories, forced versus


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non-forced scales, nature and degree of verbal description, and the

physical form or configuration.

Table 9.1

Scale Basic

Characteristic

s

Examples Advantages Disadvantage

s

Continuou

s Rating

Scale

Place a mark

on a

continuousline

Reaction to

TV

Commercials

Easy to

construct

Scoring can

be

cumbersomeunless

computerizedItemized

Rating

Scales:Likert

Scale

Degree of

agreement ona 1(Strongly

agree) to

5(strongly

Disagree)

scale

Measureme

nt of attitudes

Easy to

construct,administer,

and

understand

More time

consuming

Semantic

Differentia

l

Seven point

scale with

bipolar labels

Brand,

product,

and

company

images

Versatile Controversy

as to whether

the data are

interval

Stapel

Scale

Unipolar ten-

point scale, -5

Measureme

nt of

Easy to

construct,

Confusing

and difficult


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to +5, without

a neutral

point(zero)

attitudes

and images

administere

d over

telephone

to apply

Continuous Rating Scale: It is a non-comparative scale. Also referred

to as graphic rating scale. This measurement scale has the

respondents rate the object by placing a mark at the appropriate

position on a line that runs from one extreme of the criteria variable to

the other.

Itemized Rating Scale: A measurement scale having numbers and / or

brief descriptions associated with each category. The categories are

ordered in terms of scale position. Commonly used itemized rating

scales are Likert, Semantic Differential and Stapel Scales.

Likert Scale: A measurement scale with five response categories

ranging from strongly disagree to strongly agree which requires the

respondents to indicate a degree of agreement or disagreement with

each of a series of statements related to the stimulus objects.

Semantic Differential Scale: A 7-point rating scale with end points

associated with bi-polar labels that have semantic meaning.

Stapel Scale: A scale for measuring attributes that consists of a

single adjective in the middle of an even numbered range of values

from -5 to +5, without a neutral point (zero).


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The choice of particular scaling techniques in a given situation

should be based on theoretical and practical considerations. As a

general rule, the scaling technique used should be the one that will

yield the highest level of information feasible. Also, multiple

measures should be obtained.

Balanced Scale: A scale with an equal number of favorable and

unfavorable categories.

Forced Rating Scales: A rating scale that forces the respondents to

express an opinion because no opinion or no knowledge option is notprovided.

Number of

Categories

Although there is no single, optimal number,

traditional guidelines suggest that there should be

between five and Nine categories.Balanced versus

unbalanced

In general, the scale should be balanced to obtain

objective data.Odd or even

number of

categories

If a neutral or indifferent scale response is

possible from at least some of the respondents, an

odd number of categories should be used.Forced versus

non-forced

In situations where the respondents are expected

to have no opinion, the accuracy of data may be

improved by a non-forced scale.Verbal

Description

An argument can be made for labeling all or many

scale categories. The category descriptions should

be located as close to the response categories as

possible.Physical Form A number of options should be tried and the best

one selected.


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Construct Scale DescriptorsAttitude Very

BadBad Neither Bad

Nor GoodGood Very

GoodImportance Not at all

Important

Not

Important

Neutral Important Very

ImportantSatisfaction Very

Dissatisfied

Dissatisfied Neither

Dissatisfied

nor Satisfied

Satisfied Very

Satisfied

Purchase

Intent

Definitely

will not Buy

Probably

will not Buy

Might or

might notBuy

Probably

will Buy

Definitely

will Buy

Purchase

Frequency

Never Rarely Sometimes Often Very

Often

Multi-item scales consist of a number of rating scale items. These

scales should be evaluated in terms of reliability and validity.

Reliability refers to the extent to which a scale produces consistent

results if repeated measurements are made. Approaches to assessing

reliability include test-retest, alternative-forms, and internal

consistency. Validity, or accuracy of measurement, may be assessed

by evaluating content validity, criterion validity, and construct

validity.

Measurement Error: The variation in the information sought by the

researcher and the information generated by the measurement

process employed.


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True Scale Model: A mathematical model that provides a framework

for understanding the accuracy of measurement.

Semantic Errors: Semantic error affects the measurement in a

constant way and represents stable factors that affect the observed

score in the same way each time the measurement is made.

Reliability: The extent to which a scale produces consistent results if

repeated measurements are made on the characteristic. Approaches

for assessing reliability include the test-retest, alternative forms and

internal consistency methods.

Test-retest Reliability: An approach for assessing reliability in which

respondents are administered identical sets of scale items at two

different times under as nearly equivalent conditions as possible.

Scale Evaluation

Alternative Forms

Generalizability

Internal Consistency

Content

Test / Retest

Reliability Validity

Convergent

ConstructCriterion

NomologicalDiscriminant


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Alternative Forms Reliability: An approach for assessing reliability

that requires two equivalent forms of the scale to be constructed and

then the same respondents are measured at two different times.

Internal Consistency Reliability: An approach for assessing the

internal consistency of the set of items when several items are

summated in order to form a total score for the scale. The two

measures for internal consistency reliability are Split-half reliability

and Coefficient-Alpha.

Split-Half Reliability: A form of internal consistency reliability in whichthe items constituting the scale are divided into two halves and the

resulting half scores are correlated.

Coefficient Alpha: A measure of internal consistency reliability that is

the average of all possible split-half coefficients resulting from

different splitting of the scale items.

Validity: The extent to which difference in observed scale scores

reflect true differences among objects on the characteristic being

measured, rather than systematic or random errors. Researchers may

assess content validity, criterion validity or construct validity.

Content Validity: A type of validity sometimes called face validity that

consists of a subjective but systematic evaluation of the

representative-ness of the content of a scale for the measuring tasks

at hand.


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Criterion Validity: A type of validity that examines whether the

measurement scale performs as expected in relation to other

variables selected as meaningful criteria.

Construct Validity: A type of validity that addresses the question of

what construct or characteristic the scale is measuring. An attempt is

made to answer theoretical questions of why a scale works and what

deductions can be made concerning the theory underlying the scale.

Construct validity includes convergent, discriminant, and

Nomological validity.

Convergent Validity: A measure of construct validity that measures

the extent to which the scale correlates positively with other

measures of the same construct.

Discriminant Validity: A type of construct validity that assesses the

extent to which a measure does not correlate with other constructsfrom which it is supposed to differ.

Nomological Validity: A type of validity that assesses the relationship

between theoretical constructs. It seeks to confirm significant

correlations between the constructs as predicted by theory.

Generalizability: The degree to which a study based on a sample

applied to a universe of generalization.

In international marketing research, special attention should be

devoted to determining equivalent verbal descriptors in different


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languages and cultures. The researcher has a responsibility to both

the client and respondents to ensure the applicability and usefulness

of the scales. The Internet and computers are useful for developing

and testing continuous and itemized rating scales, particularly multi-

item scales.

Chapter 10

To collect quantitative primary data, a researcher must design a

questionnaire or an observation form. A questionnaire has threeobjectives. It must translate the information needed into a set of

specific questions the respondents can and will answer. It must

motivate respondents to complete the interview. It must also minimize

response error.

Questionnaire: A structured technique for data collection thatconsists of a series of questions written or verbal that a respondent

answers.

Designing a questionnaire is an art rather than a science. The process

begins by specifying:

1) The information needed

2) The type of Interviewing method

3) To decide on the content of the individual question

4) The question should overcome the respondents inability and

unwillingness to answer


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Double barreled question: A single question that attempts to cover

two issues. Such questions can be confusing to respondents and

result in ambiguous responses.

Respondents may be unable to answer if they are not informed,

cannot remember, or cannot articulate the response.

Filter Question: An initial question in a questionnaire that screens

potential respondents to ensure that they meet the requirements of

the sample.

Telescoping: A psychological phenomenon that takes place when an

individual telescopes or compresses time by remembering an event

as occurring more recently than it actually occurred.

The unwillingness of the respondents to answer must also be

overcome. Respondents may be unwilling to answer if the questionrequires too much effort, is asked in a situation or context deemed

inappropriate, does not serve a legitimate purpose, or solicits

sensitive information.

Then comes the decision regarding the question structure (step 5).

Questions can be unstructured (open-ended) or structured to a

varying degree. Structured questions include multiple choice,

dichotomous questions and scales.

Un-structured Questions: Open-ended questions that respondents

answer in their own words.


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Structured Questions: Questions that pre-specify the set of response

alternative and the response format. A structured question could be

multiple-choice or a scale.

Order or position bias: A respondents tendency to check an

alternative merely because it occupies a certain position or is listed in

a certain order.

Dichotomous Questions: A structured question with only two

response alternatives such as Yes or No.

Determining the wording of each question (step 6) involves defining

the issue, using ordinary words, using unambiguous words, and

using dual statements. The researcher should avoid leading

questions, implicit alternatives, implicit assumptions, and

generalizations and estimates.

Once the questions have been worded, the order in which they will

appear in the questionnaire must be decided (step 7). Special

consideration should be given to opening questions, type of

information, difficult questions, and the effect on subsequent

questions. The questions should be arranged in a logical order.

Leading Questions: A question that gives the respondent a clue as to

what answer is desired or leads the respondent to answer in a certain

way.


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placement of directions, color-coding, easy to read format, and cost.

Last but not the least is pre-testing (step 10).

Pre-testing: The testing of the questionnaire on a small sample of

respondents for the purpose of improving the questionnaire by

identifying and eliminating potential problems.

Important issues are the extent of pre-testing, nature of respondents,

type of interviewing method, type of interviewers, sample size,

protocol analysis and debriefing, and editing and analysis.

The design of observational forms requires explicit decisions about

what is to be observed and how that behavior is to be recorded. It is

useful to specify the who, what, when, where, why and way of the

behavior to be observed.

The questionnaire should be adapted too the specific culturalenvironment and should not be biased in terms of any one culture.

Also, the questionnaire may have to be suitable for administration by

more than one method because different interviewing methods may

be used in different countries. Several ethical issues related to the

researcher-respondent relationship and researcher-client relationship

may have to be addressed. The Internet and computers can greatly

assist the researcher in designing sound questionnaires and

observational forms.

Chapter 11


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Information about the characteristic of a population may be obtained

by conducting either a sample or a census. Budget and time limits,

large population size, and small variance in the characteristic of

interest favour the use of a sample. Sampling is also preferred when

the cost of sampling error is low, the cost of non-sampling error is

high, the nature of measurement is destructive, and attention must be

focused on individual cases. The opposite set of conditions favour

the use of census.

Population: The aggregate of all the elements, sharing some commonset of characteristics that comprises the universe for the purpose of

the marketing research problem.

Census: A complete enumeration of the elements of population or

study objects.

Sample: A sub-group of the elements of the population selected for

participation in the study.

Sampling design begins by defining the target population in terms of

elements, sampling units, extent, and time.

Target Population: The collection of elements or objects that possess

information sought by the researcher and about which inferences are

to be made.


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Element: Object that possess the information sought by the

researcher and about which inferences are to be made.

Sampling Unit: The basic unit containing the elements of the

population to be sampled.

Then the sampling frame should be determined. A sampling frame is a

representation of the elements of the target population. It consists of

a list of directions for identifying the target population. At this stage,

it is important to recognize any sampling frame errors that may exist.

The next steps involve selecting a sampling technique anddetermining the sample size. In addition to quantitative analysis,

several qualitative considerations should be taken into account in

determining the sampling size. Finally, execution of the sampling

process requires detail specification for each step in the sampling

process.

Sampling Frame: A representation of the elements of the target

population. It consists of a list or set of directions for identifying the

target population.

Bayesian Approach: A selection method in which elements are

selected sequentially. This approach explicitly incorporates prior

information about population parameters as well as the costs and

probability associated with making wrong decisions.

Sampling with replacement: A sampling technique in which an

element can be included in the sample more than once.


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Sampling without replacement: A sampling technique in which an

element cannot be included in the sample more than once.

Sample Size: A number of elements to be included in a study.

Sampling techniques may be classified as non-probability and

probability techniques.

Non-probability Sampling: Sampling techniques that do not use

chance selection procedures. Rather they rely on the personal judgment of the researcher.

Probability Sampling: A sampling procedure in which each element of

the population has a fixed probabilistic chance of being selected for

the sample.

Non-probability sampling techniques rely on the researchers

judgment. Consequently, they do not permit an objective evaluation

of the precision of the sample results, and the estimates obtained are

not statistically projectable to the population. The commonly used

non-probability sampling techniques include convenience sampling,

judgmental sampling, quota sampling, and snowball sampling.

Convenience sampling: A non-probability sampling technique that

attempts to obtain a sample of convenient elements. The selection of

sampling units is left primarily to the interviewer.


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Judgmental sampling: A form of convenience sampling in which the

population elements are purposely selected based on the judgment of

the researcher.

Quota sampling: A non-probability sampling technique that is a two-

stage restricted judgmental sampling. The first stage consists of

developing control categories or quotas of population elements. In

the second stage, sample elements are selected based on

convenience or judgment.

Snowball sampling: A non-probability sampling technique in which aninitial group of respondents are selected randomly. Subsequent

respondents are selected based on the referrals or information

provided by the initial respondents. This process may be carried out

in waves by obtaining referrals from referrals.

In probability sampling techniques, sampling units are selected bychance. Each sampling unit has a non-zero chance of being selected

and the researcher can pre-specify every potential sample of a given

size that could be drawn from the population, as well as the

probability of selecting each sample. It is also possible to determine

the precision of the sample estimates and inferences and make

projections to the target population. Probability sampling technique

includes simple random sampling, systematic sampling, stratified

sampling, cluster sampling, sequential sampling, and double

sampling.


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and the probability of selecting a sampling unit in a selected cluster

varies inversely with the size of the cluster.

Sequential Sampling: A probability sampling technique in which the

elements are sampled sequentially, data collection and analysis are

done at each stage, and a decision is made as to whether additional

population element should be sampled.

Double Sampling: A sampling technique in which certain population

elements are sampled twice.

Table 11.3Technique Strengths WeaknessesNon-

probability

SamplingConvenience

Sampling

Least Expensive, Least time

consuming, most convenient

Selection bias, sample not

representative, not recommended

for descriptive or causal researchJudgmental

Sampling

Low cost, Not time consuming,

convenient

Does not allow generalization,

subjective

Quota

Sampling

Sample can be controlled for

certain characteristics

Selection bias, no assurance of

of representativeness

Snowball

Sampling

Can estimate rare

characteristics

Time Consuming

ProbabilitySamplingSimple

Random

SamplingSystematic Can increase representative-

ness, easier to implement that


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Sampling SRS, sampling frame notnecessary

Stratified

Sampling

Includes all important

subpopulations, precision

Cluster

Sampling

Easy to implement, cost

effective

Exhibit 11.1

The choice between probability and non-probability sampling should

be based on the nature of the research, the degree of error tolerancethe relative magnitude of sampling and non-sampling errors, the

variability in the population, and statistical and operational

considerations.

When conducting international marketing research, it is desirable to

achieve comparability in sample composition and representativeness,

even though this may require the use of different sampling

techniques in different countries. It is unethical and misleading to

treat non-probability samples as probability sample and project the

results to a target population. The Internet and computers can be

used to make the sampling design process more effective and

efficient.

Chapter 15


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Basic data analysis provides valuable insights and guides the rest of

the data analysis as well as the interpretation of the results. A

frequency distribution should be obtained for each variable in the

data.

Frequency Distribution: A mathematical distribution whose objective

is to obtain a count of the number of responses associated with

different values of one variable and to express these counts in

percentage terms.

This analysis produces a table of frequency counts, percentages, andcumulative percentages for all the values associated with that

variable. It indicates the extent of out of range, missing, or extreme

values. The mean, mode, and median of a frequency distribution are

measures of central tendency.

Measures of location: A statistic that describes a location within adata set. Measures of central tendency describe the center of the

distribution.

Mean: The average; that value obtained by summing all elements in a

set and dividing by the number of elements.

Mode: A measure of central tendency given as the value that occurs

the most in a sample distribution.

Median: A measure of central tendency given as the value above

which half of the values fall and below which half of the values fall.


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The variability of the distribution is described by the range, the

variance, or standard deviation, coefficient of variation, and inter-

quartile range.

Measures of variability: A statistic that indicates the distributions

dispersion.

Range: The difference between the largest and smallest values of a

distribution.

Inter-quartile range: The range of a distribution encompassing the

middle 50 percent of the observations. It is the difference between the

75 th and 25 th percentile. For a set of data points arranged in order of

magnitude, the pth percentile is the value that has p percent of the

data points below it and (100-p) percent above it. If all the data points

are multiplied by a constant, the inter-quartile range is multiplied bythe same constant.

VALUE LABEL Value Frequency

(N)

Percenta

ge

Cumulative

PercentageVery Unfamiliar 1 0 0 0

2 2 6.9 6.93 6 20.7 27.64 6 20.7 48.35 3 10.3 58.66 8 27.6 86.2

Very Familiar 7 4 13.8 100Total 30 100

Range: 7 2 = 5


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Inter-quartile Range: 6 3 = 3

The difference between the mean and an observed value is called the

deviation from the mean.

Variance: The mean squared deviation of all the values from the

mean. The variance can never be negative. When the data points are

clustered around the mean, the variance is small. When the data

points are scattered, the variance is large.

Standard Deviation: The square root of the variance. The standard

deviation of a sample, s, is calculated as:

=

=

n

i n

X X s

1

2

1)(

By dividing by n-1, instead of n, we compensate for the smaller

variability observed in the sample.

As Mean X (Bar) = (2 x 2 + 6 x 3 +_______+ 4 x 7) / 29

= 4.724

Variance, s 2 = 2.493

Standard Deviation, s = 1.579

Coefficients of variation: A useful expression in sampling theory for

the standard deviation as a percentage of the mean. It is the ratio of

the standard deviation to the mean. It is measure of relative

variability. Meaningful only for variable measured in ratio scale. If a


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characteristic shows good variability, then perhaps the market could

be segmented based on that characteristics.

Skewness and kurtosis provide an idea or measure of the shape of

the distribution.

Skewness: A characteristic of a distribution that assesses its

symmetry about the mean. Skewness is the tendency of the

deviations from the mean to be larger in one direction than in the

other, i.e., one tail of the distribution is heavier than the other.

Kurtosis: A measure of the relative peaked-ness or flatness of the

curve defined by the frequency distribution. The kurtosis of a normal

distribution is zero. If the kurtosis is positive, then the distribution is

more peaked than a normal distribution. A negative value means a

flatter distribution. If distribution is highly peaked or flat, then

statistical procedures that assume normality should be used withcaution.

INTRODUCTION TO HYPOTHESIS

Hypothesis, one simply means a mere assumption or some

supposition to be proved or disproved.

For a Researcher hypothesis is a formal question that he intends

to resolve. A Research hypothesis is a predictive statement,

capable of being tested by scientific methods, that relates an

independent variable to some dependent variable. Its main

function is to suggest new experiments and observations


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Example:- Students who receive counseling will show a greater

increase in creativity than students not receiving counseling

Or

The automobile A is performing as well as automobile B.

These are hypotheses capable of being objectively verified and

tested. Thus, we may conclude that a hypothesis states what we

are looking for and it is a preposition which can be put to a test

to determine its validity.

General Procedure for Hypothesis Testing:

1. Formulate the null hypothesis H 0 and the alternativehypothesis H 1.

2. Select an appropriate statistical technique and the

corresponding test statistic.

Choose the level of significance, .

4. Determine the sample size and collect the data.

Calculate the value of the test statistic.5. Determine the probability associated with the test

statistic under the null hypothesis, using the sampling

distribution of the test statistic. Alternatively, determine the

critical values associated with the test statistics that divide the

rejection and non-rejection regions.

6. Compare the probability associated with the test

statistic with the level of significance specified. Alternatively,

determine whether the test statistic has fallen into the rejection or

the non-rejection region.

7. Make the statistical decision to reject or not reject

the null hypothesis.


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8. Express the statistical decision in terms of the

marketing research problem.

A General Procedure for Hypothesis Testing

Formulate Null hypothesis and Alternative Hypothesis.

Select an appropriate test

Choose the level of Significance

Collect data and calculate the test statistic

Determine the probability Determine the critical valueassociated with the test statistic of the test statistic.

Compare probability with the Determine if TSCR falls into

level of significance rejection or non rejection region

Reject or do not reject null hypothesis

Draw a management research conclusion

*TSCR: Critical value of Test Statistic

Basic concepts Concerning Testing of Hypothesis

Null hypothesis: A statement in which no difference or effect is

expected. If the null hypothesis is not rejected, no changes will be

made.


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Alternative hypothesis: A statement that some difference or effect is

expected. Accepting the alternative hypothesis will lead to changes in

opinions or actions.

Null Hypothesis:- If we are to compare method A with method Babout its superiority and if we proceed on the assumption that

both methods are equally good , then this assumption is termed

as Null Hypothesis. As against this, we may think that the

method A is superior or the method B is inferior, we are stating

what is termed as Alternative Hypothesis.

Level of Significance:- It is always some %(usually 5%). If we

take the significance level at 5%, then null hypothesis will be

rejected.

One-tailed Test: A test of the null hypothesis where the

alternative hypothesis is expressed directionally. A one tailed

test would be used when we are to test, say, whether the

population mean is either lower than or higher than some

hypothesized value. For example: The proportion of internet

users who use the internet for shopping is greater than 0.40.

The Hypothesis for this example would be

H0 : 0.40

H1 : > 0.40 If the null hypothesis is rejected, then the alternative hypothesis

H1 will be accepted and the new Internet shopping service will be

introduced.

Acceptance region A: Z > -1.645


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Rejection region R: Z < -1.645

Two-Tailed Test:- A test of null hypothesis where the alternative

hypothesis is not expressed directionally. A two tailed test

rejects the null hypothesis if, say, the sample mean is

significantly higher or lower than the hypothesized value of the

mean of the population. If the significance level is 5% & the two

tailed test is to be applied, the probability of the rejection area

will be 0.05 & that of the acceptance region will be 0.95.

For example: The proportion of internet users who use the

internet for shopping is different from 0.40. The Hypothesis for this example would be

H0 : = 0.40

H1 : 0.40

The one-tailed test is used more often than a two-tailed test.

Test statistic: A measure of how close the sample has come to the

null hypothesis. It often follows a well-known distribution, such as the

normal, t, or chi-square distribution. For example the z statistic which

follows the standard normal distribution would be appropriate.

Z = (p - )/ p

When we draw inference about a population there is a risk of incorrectconclusion. Two types of errors can occur.

Type I error: Also known as alpha error, it occurs when the sample

results lead to the rejection of a null hypothesis that is in fact true.


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Internet Usage Male Female Row TotalLight 5 10 15Heavy 10 5 15Column Total 15 15

Contingency Table: A cross-tabulation table. It contains a cell for

every combination of categories of the two variables.

The chi-square statistic provides a test of the statistical significance

of the observed association in cross-tabulation.

Chi-square statistic: The statistic used to test the statistical

significance of the observed association in a cross-tabulation. It

assists us in determining whether a systematic association exists

between the two variables.

Chi-square Distribution: A skewed distribution whose shape depends

solely on the number of degrees of freedom. As the number of

degrees of freedom increases, the chi-square distribution becomes

more symmetrical.

The null Hypothesis is that there is no association between the

variables. The expected cell frequencies, denoted by f e are compared

to the actual observed frequencies, f o, found in the cross-tabulation to

calculate the chi-square statistic.

For r rows and c columns and n observations, the expected cell

frequency for each cell is given by

Fe = (n r n c )/n


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After calculating above, we calculate value of chi-square as

fe

fe fo =

2

2

)(

333.32 =

In case of a chi-square statistic associated with a cross tabulation,

the number of degrees of freedom is given by:

Df = (r-1) x (c-1)

The null hypothesis (H 0) of no association between the two variableswill be rejected only when the calculated value of the test statistic is

greater than the critical value of the chi-square distribution with the

appropriate degrees of freedom.

As the number of degrees of freedom increases, the chi-square

distribution becomes more symmetrical.

For one degree of freedom, the value for an upper-tail area of 0.05 is

3.841.

This indicates that for 1 degree of freedom, the probability of

exceeding a chi-square value of 3.841 is 0.05. i.e. at 0.05 level of

significance with 1 degree of freedom, the critical value of the chi-

square statistic is 3.841.

For a cross-tabulation of 2 x 2, df = (2-1) x (2-1) =1. The calculate

chi-square value is 3.333, which is less than critical value of 3.841. So,

the null hypothesis of no association cannot be rejected, indicating

that the association is not statistically significant at the 0.05 level.

This lack of significance is mainly due to small sample size of 30. If

sample size would have been 300, then let each entry in table


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multiplied by 10, then value of chi-square statistic would be multiplied

by 10 and would be 33.33, which is significant at 0.05 level.

For frequency observations less than 5, chi-square analysis should

not be conducted, or when table is 2 x 2. Then phi- coefficient should

be applied.

The phi-coefficient, contingency coefficient, Cramers V, and the

lambda coefficient provide measures of the strength of association

between the variables.

Phi-coefficient: A measure of the strength of association in thespecial case of a table with two rows and two columns.

n

2 =

It takes value of 0 when there is no association. When variables are

perfectly associated, phi takes value of 1. All values of phi falls

between -1, 0, and 1. -1 represents perfect negative correlation. Phi for

above example is

30333.3=

= 0.333So the association is not very strong.

Contingency coefficient (C): A measure of the strength of association

in a table of any size.

Cramers V: A measure of the strength of association used in tables

larger than 2 X 2.


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Lambda Coefficient: A measure of the percentage improvement in

predicting the value of the dependent variable, given the value of the

independent variable in contingency table analysis. Lambda also

varies between 0 and 1.

Symmetric lambda: The symmetric lambda does not make an

assumption about which variable is dependent. It measures the

overall improvement when prediction is done in both directions.

Tau b: Test statistic that measures the association between twoordinal level variables. It makes an adjustment for ties and is most

appropriate when the table of variables is square.

Tau c: Test statistic that measures the association between two

ordinal level variables. It makes an adjustment for ties and is most

appropriate when the table of variables is not square but a rectangle.

Gamma: Test statistic that measures the association between two

ordinal level variables. It does not make an adjustment for ties.

Parametric and non-parametric tests are available for testing

hypothesis related to differences.

Parametric tests: Hypothesis-testing procedures that assume that the

variables of interest are measured on at least an interval scale.


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Non-Parametric tests: Hypothesis-testing procedures that assume

that the variables of interest are measured on a nominal or ordinal

scale.

The samples are independent if they are drawn randomly from

different populations. For example, data pertaining to males and

females are treated as independent samples. The samples are paired

when the data for the two samples relate to the same group of

respondents.

HYPOTHESIS TESTSPARAMETRIC

TESTS

NONPARAMETRICTESTS

ONE SAMPLEt-testz-test

ONE SAMPLEChi square

k-sTWO SAMPLES TWO SA

Independent testsTwo group t test

Z - tsst

Paired samplesPaired t-test


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In the parametric case, the t-test is used to examine hypothesis

related to the population mean. Different forms of the t-test are

suitable for testing hypothesis based on one sample, two

independent samples, or paired samples.

T test: A univariate hypothesis test using the t distribution, which is

used when the standard deviation is unknown and the sample size is

small.

Hypothesis tests

Parametric tests

( Non-parametric tests

Onesample

Independentsample

Onesample

Twosample

Independentsample Pairedsample

T testZ test

paired t- test Chi- squareMann-whitneyMedianK-S

SignWilcoxonMcNemar Chi-square

Chi- squareK-s

Runs binomial

Twosample

Two-groupt- test

z test

PairedSamples


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4. Take 1 or 2 samples and compute the mean and standard

deviation for each sample.

5. Calculate the t statistic assuming H 0 is true.

6. Calculate the degrees of freedom and estimate the

probability of getting a more extreme value of the statistic from

Table. Calculate the critical value of the t statistic.

7. If probability computed above is smaller than significance

level, reject H 0. If probability is larger, do not reject H 0. If

calculated value of t-statistic is larger than the critical value,

reject H 0. If calculated value of t-statistic is smaller than the

critical value, accept H 0.

8. Express the conclusion reached by the t test in terms of

the marketing research problem

RESPONDENT

NUMBER

SEX

FAMILIARITY

INTERNET

USAGE

ATTITIUDE

TOWARDS

INTERNET

ATTITUDE

TOWARDS

TECHNOLOGY

USAGE OFINTERNET:S

HOPPING

USAGE OFINTERNET:B

ANKING1 1 7 14 7 6 1 12 2 2 2 3 3 2 23 2 3 3 4 3 1 24 2 3 3 7 5 1 25 1 7 13 7 7 1 16 2 4 6 5 4 1 27 2 2 2 4 5 2 28 2 3 6 5 4 2 29 2 3 6 6 4 1 2

10 1 9 15 7 6 1 211 2 4 3 4 3 2 212 2 5 4 6 4 2 213 1 6 9 6 5 2 114 1 6 8 3 2 2 215 1 6 5 5 4 1 216 2 4 3 4 3 2 217 1 6 9 5 3 1 118 1 4 4 5 4 1 2


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19 1 7 14 6 6 1 120 2 6 6 6 4 2 221 1 6 9 4 2 2 222 1 5 5 5 4 2 123 2 3 2 4 2 2 224 1 7 15 6 6 1 1

25 2 6 6 5 3 1 226 1 6 13 6 6 1 127 2 5 4 5 5 1 128 2 4 2 3 2 2 229 1 4 4 5 3 1 230 1 3 3 7 5 1 2

Some statements for a single variable are:

The market share for new product will exceed 15 percent.

80 percent of dealers will prefer the new pricing policy.

These statements are converted to null hypothesis that can be tested

by one-sample test such as t-test or the z-test.

Suppose we want to test the hypothesis that the mean familiarity with

the internet rating exceeds 4.0, the neutral value on a 7-point scale

(1- very unfamiliar, 7- very familiar).A significance level of =0.05 is selected. The hypothesis may be

formulated as:

H0 : 0.40

H1 : > 0.40

Standard deviation of the sample mean, X, is estimated as s X = s / n .

Then,

t = (X ) / s X

is t distributed with n-1 degrees of freedom.

s X = 1.579 / 29 = 1.579/5/385 = 0.293

t= (4.724-4.0)/0.293=0.724/0.293 =2.471

Here, n-1 = 29-1 = 28


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Probability of getting a more extreme value than 2.471 is less than

0.05. It implies that the critical t value for 28 degrees of freedom and a

significance level of 0.05 is 1.7011, which is less than the calculated

value. Hence null hypothesis is rejected. The familiarity level does

exceed 4.0.

z test: A univariate hypothesis test using the standard normal

distribution.

Independent samples: Two samples that are not experimentallyrelated. The measurement of one sample has no effect on the values

of the second sample.

F test: A statistical test of the equality of the variances of two

populations.

F statistic: The F statistic is computed as the ratio of two sample

variance.

F distribution: A frequency distribution that depends upon two sets of

degrees of freedom the degrees of freedom in the numerator and

the degrees of freedom in the denominator.

Paired samples: In hypothesis testing, the observations are paired so

that the two sets of observations relate to the same respondents.


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Paired samples t test: A test for differences in the means of paired

samples.

In the non-parametric case, popular one sample test include the

Kolmogorov-Smirnov, chi-square, runs test, and the binomial test. For

two independent non-parametric samples, the Mann-Whitney U test,

median test, and the Kolmogorov-Smirnov test can be used. For

paired samples the Wilcoxon matched-pairs signed-ranks test and the

sign test are useful for examining hypothesis related to measures of location.

Kolmogorov-Smirnov one sample test: A one sample non-

parametric goodness of fit test that compares the cumulative

distribution function for a variable with a specified distribution.

Runs test: A test of randomness for a dichotomous variable.

Binomial test: A goodness of fit statistical test for dichotomous

variables. It tests the goodness of fit of the observed number of

observations in each category to the number expected under a

specified binomial distribution.

Mann-Whitney U test: A statistical test for a variable measured on an

ordinal scale, comparing the differences in the location of two

populations based on observations from two independent samples.


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Two-sample median test: Non-parametric test statistic that

determines whether two groups are drawn from populations with the

same median. This test is not as powerful as the Mann-Whitney U.

Kolmogorov-Smirnov two sample test: Non-parametric test statistic

that determines whether two distributions are same. It takes into

account any differences in the two distributions including median,

dispersion, and skewness.

Wilcoxon matched pairs signed ranks test: A non-parametric test that

analyzes the differences between the paired observations, taking intoaccount the magnitude of the differences.

Sign test: A non-parametric test for examining differences in the

location of two populations based on paired observations that

compares only the signs of the differences between pairs of variables

without taking into account the magnitude of the differences.

Table 15.19

Chapter 16

In ANOVA and ANCOVA, the dependent variable is metric and the

independent variables are all categorical, or combination of

categorical and metric variables. One way ANOVA involves a single

independent categorical variable. Interest lies in testing the null

hypothesis that the category means are equal in the population.


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Analysis of variance (ANOVA): A statistical technique for examining

the differences among means for two or more populations.

Factors: Categorical independent variables. The independent

variables must be all categorical (non-metric) to use ANOVA.

Treatment: In ANOVA, particular combination of factor levels or

categories.

One-way analysis of variance: An ANOVA technique in which there is

only one factor.

The total variation in the dependent variable is decomposed into two

components: variation related to the independent variable, and

variation related to an error. The variation is measured in terms of the

sum of squares corrected for the mean (SS). The mean square is

obtained by dividing the SS by the corresponding degree of freedom(df). The null hypothesis of equal means is tested by an F statistic,

which is the ratio of the mean square relating the independent

variable to the mean square related to error.

For example: A major department store chain wanted to examine the

effect of the level of in-store promotion and a storewide coupon on

sales. In-store promotion was varied at three levels: high(1),

medium(2), and low(3). Couponing was manipulated at two levels.

Either a $20 storewide coupon was distributed to potential shoppers

(denoted by 1) or it was not (denoted by 2). In-store promotion and

couponing were crossed, resulting in a 3 x 2 design with six cells.


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Thirty stores were randomly selected, and five stores were randomly

assigned to each treatment condition. The experiment was run for two

months. Sales in each store were measured, normalized to account

for extraneous factors (store size, traffic, etc) and converted to a 1-to-

10 scale. In addition a qualitative assessment was made of the relative

affluence of the clientele of each store, again using a 1-to-10 scale. In

these scales, higher numbers denote higher sales or more affluent

clientele.

Table 16.2 carries the data display.

Suppose that only one factor, namely in-store promotion, was

manipulated. The department store is attempting to determine the

effect of in-store promotion (X) on sales (Y).

The null hypothesis is that the category means are equal:

H0: 1 = 2 = 3 Here represents average sales.

We calculate F statistic as F=17.944

The critical value of F is 3.35 for = 0.05

Because the calculated value of F is greater than the critical value, we

reject the null hypothesis. We conclude that the population means for

the three levels of in-store promotion are indeed different. The relative

magnitudes of the means for the three categories indicate that a high

level of in-store promotion leads to significantly higher sales.


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Coupon Level, In-store Promotion, Sales, and Clientele Rating

StoreNo.

CouponLevel

In-StorePromotion Sales

ClienteleRating

1 1 1 10 92 1 1 9 103 1 1 10 84 1 1 8 45 1 1 9 66 1 2 8 87 1 2 8 48 1 2 7 109 1 2 9 6

10 1 2 6 911 1 3 5 812 1 3 7 913 1 3 6 614 1 3 4 1015 1 3 5 416 2 1 8 1017 2 1 9 618 2 1 7 819 2 1 7 420 2 1 6 921 2 2 4 622 2 2 5 823 2 2 5 10

24 2 2 6 425 2 2 4 926 2 3 2 427 2 3 3 628 2 3 2 1029 2 3 1 930 2 3 2 8

Apply one-way ANOVA as:

1. Select ANALYZE from the SPSS menu bar.

2. Click COMPARE MEANS and then ONE-WAY ANOVA.

3. Move Sales into the DEPENDENT LIST box.

4. Move In-Store Promotion to the FACTOR box.

5. Click OPTIONS.

6. Click DESCRIPTIVE.


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7. Click CONTINUE.

8. Click OK.

After applying SPSS, we found that sample means with values of 8.3,

6.2 and 3.7

Stores with a high level of in-store promotion have the highest

average sales (8.3) and stores with a low level of in-store promotion

have the lowest average sales (3.7).

n-way analysis of variance involves the simultaneous examination of

two or more categorical independent variables. n-way analysis of variance provides an ANOVA model where two or more factors are

involved.

A major advantage is that the interactions between the independent

variables can be examined. The significance of the overall effect,

interaction terms, and the main effects of individual factors areexamined by appropriate F tests. It is meaningful to test the

significance of main effects only if the corresponding interaction

terms are not significant.

ANCOVA includes at least one categorical independent variable and

at least one interval or metric independent variable. The metric

independent variable or covariate is commonly used to remove

extraneous variation from the dependent variable.

Analysis of covariance (ANCOVA): An advanced analysis of variance

procedure in which the effects of one or more metric-scaled


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extraneous variables are removed from the dependent variable before

conducting the ANOVA.

COVARIATE: A metric independent variable used in ANCOVA.

When analysis of variance is conducted on two or more factors,

interactions can arise. An interaction occurs when the effect of an

independent variable on a dependent variable is different for different

categories or levels of another independent variable.

Decomposition of the total variation: In one way ANOVA, separationof the variation observed in the dependent variable into the variation

due to the independent variables plus the variation due to error.

Interaction: When assessing the relationship between two variables,

an interaction occurs if the effect of X1 depends on the level of X2 and

vice-versa.

Multiple n2: The strength of the joint effect of two (or more) factors, or

the overall effect.

Significance of the overall effect: A test that some differences exist

between some of the treatment groups.

Significance of the interaction effect: A test of the significance of the

interaction between two or more independent variables.


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Significance of the main effect: A test of the significance of the main

effect for each individual factor.

If the interaction is significant, it may be ordinal or disordinal.

Ordinal Interaction: An interaction where the rank order of the effects

attributable to one factor does not change across the levels of the

second factor.

Dis-ordinal Interaction: The change in the rank order of the effects of

one factor across the levels of another.

Dis-ordinal interaction may be of a non-crossover or crossover type.

In balanced designs, the relative importance of factor in explaining

the variation in the dependent variable is measured by omega square

( 2).

Omega squared ( 2): A measure indicating the proportion of the

variation in the dependent variable explained by a particular

independent variable or factor.

Multiple comparisons in the form of a priori or a posteriori contrast

can be used for examining differences among specific means.

Contrasts: In ANOVA, a method of examining differences among two

or more means of the treatment groups.


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A priori contrasts: Contrasts that are determined before conducting

the analysis, based on the researchers theoretical framework.

A posteriori contrasts: Contrasts made after the analysis. These are

generally multiple comparison tests.

Multiple Comparison test: A posteriori contrasts that enables the

researcher to conduct generalized confidence intervals that can be

used to make pair-wise comparisons of all treatment means.

In repeated measures analysis of variance, observations on eachsubject are obtained under each treatment condition. This design is

useful for controlling for the difference in subjects that exists prior to

the experiment.

Repeated measures ANOVA: An ANOVA technique used when

respondents are exposed to more than one treatment condition andrepeated measurements are obtained.

Non-metric analysis of variance involves examining the differences in

the central tendencies of two or more groups when the dependent

variable is measured on an ordinal scale.

Non-metric ANOVA: An ANOVA technique for examining the

differences in the central tendencies of more than two groups when

the dependent variable is measured on an ordinal scale.


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K sample median test: non-parametric test is used to examine the

differences among groups when the dependent variable is measured

on an ordinal scale.

Kruskal-Wallis one way analysis of variance: A non-metric ANOVA

test that uses the rank value of each case, not merely its location

relative to the median.

Multi-variate analysis of variance (MANOVA) involves two or more

metric dependent variables.

Multivariate Analysis of variance (MANOVA): An ANOVA technique

using two or more metric dependent variables.

Figure 16.1

Chapter 17

The product moment correlation coefficient r, measures the linear

association between two metric (interval or ratio scaled) variables. Its

square, r 2, measures the proportion of variation in one variable

explained by the other.

Product moment correlation (r): A statistic summarizing the strength

of association between two metric variables (interval or ratio scaled).


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Here r is close to 1.0. This means that respondents duration of

residence in the city is strongly associated with their attitude toward

the city. The positive sign of r implies a positive relationship; the

longer the duration of residence, the more favorable the attitude and

vice versa.

When it is computed for a population than a sample, the product

moment correlation is denoted by (rho). The coefficient r is an

estimator of . The statistical significance of the relationship between

two variables measured by using r can be conveniently tested. The

hypotheses are:

H0: = 0H1: 0

t-statistic would be applied with n-2 degrees of freedom.

Here t is calculated as 8.414 and the degrees of freedom are 12 - 2=10.

From t-distribution table, the critical value of t for a two-tailed test and

= 0.05 is 2.228.

Hence null hypothesis of no relationship between X and Y is rejected.

This along with positive value of r indicates the attitude toward the

city is positively related to the duration of residence in the city. The

high value of r indicates that this relationship is strong.

Steps in SPSS are:

1. Select ANALYZE from the SPSS menu bar.

2. Click CORRELATE and then BIVARIATE.

3. Move Attitude into the VARIABLES box. Then move

duration into the VARIABLES box.

4. Check PEARSON under CORRELATION COEFFICIENTS.


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obtained by computing ratio of SS reg to SS y. The standard error of

estimate is used to assess the accuracy of prediction and may be

interpreted as a kind of average error made in predicting Y from the

regression equation.

Regression Analysis: A statistical procedure for analyzing associative

relationships between a metric dependent variable and one or more

independent variables.

Bivariate regression: A procedure for deriving a mathematical

relationship, in the form of an equation, between a single metricdependent variable and a single metric independent variable.

Least-square procedure: A technique for fitting a straight line to a

scattergram by minimizing the square of the vertical differences of all

the points from the line.

Multiple regressions involve a single dependent variable and two or

more independent variables. The partial regression coefficient, b 1

represents the expected change in Y, when X 1 is changed by one unit

and X 2 through X K are held constant. The strength of association is

measured by coefficient of multiple determination, R 2. The

significance of the overall regression equation may be tested by the

overall F test. Individual partial regression coefficients may be tested

for significance using the t-test or the incremental F test. Scatter

grams of the residuals, in which the residual are plotted against

predicted values, Y i, time, or predictor variables are useful for


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examining the appropriateness of the underlying assumptions and

the regression model fitted.

Multiple regression: A statistical technique that simultaneously

develops a mathematical relationship between two or more

independent variables and an interval-scaled dependent variable.

Multiple regression model: An equation used to explain the results of

multiple regression analysis.

Residual: The differences between the observed value of Yi and thevalu

research methodology ver5

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