marketing research 4
TRANSCRIPT
4-1
A Comparison of Primary & Secondary Data
Primary Data Secondary Data
Collection purpose For the problem at hand For other problemsCollection process Very involved Rapid & easyCollection cost High Relatively lowCollection time Long Short
Table 4.1
4-2
Uses of Secondary Data
Identify the problemBetter define the problemDevelop an approach to the problemFormulate an appropriate research design (for example, by identifying the key variables)Answer certain research questions and test some hypothesesInterpret primary data more insightfully
4-3
A Classification of Secondary Data
Secondary Data
Ready to Use
Requires Further Processing
PublishedMaterials
Computerized Databases
Syndicated Services
Fig. 4.1
Internal External
4-4
A Classification of Published Secondary Sources
StatisticalData
Guides Directories Indexes Census Data
Other Government Publications
Fig. 4.2
Published Secondary Data
General Business Sources
Government Sources
4-5
A Classification of Computerized Databases
Bibliographic Databases
Numeric Databases
Full-Text Databases
Directory Databases
Special- Purpose Databases
Fig. 4.3
Computerized Databases
Online Off-LineInternet
4-6
Syndicated Services: ConsumersFig. 4.4 cont.
Psychographic& Lifestyles General Advertising
Evaluation
Households / Consumers
Scanner Diary Panels with Cable TV
Surveys Volume Tracking Data
Scanner Diary Panels
Electronic scanner servicesPurchase Media
Panels
4-7
Syndicated Services: Institutions
Audits
Direct Inquiries
Clipping Services
Corporate Reports
Fig. 4.4 cont.Institutions
Retailers Wholesalers Industrial firms
4-8
A Classification of Marketing Research Data
Survey Data
Observational and Other Data
Experimental Data
Fig. 5.1
Qualitative Data Quantitative Data
Descriptive Causal
Marketing Research Data
Secondary Data Primary Data
4-9
Qualitative vs. Quantitative Research
Qualitative Research
To gain a qualitative understanding of the underlying reasons and motivations
Small number of non- representative cases
Unstructured
Non-statistical
Develop an initial understanding
Objective
Sample
Data Collection
Data Analysis
Outcome
Quantitative Research
To quantify the data and generalize the results from the sample to the population of interest
Large number of representative cases
Structured
Statistical
Recommend a final course of action
Table 5.1
4-10
A Classification of Qualitative Research Procedures
Association Techniques
Completion Techniques
Construction Techniques
Expressive Techniques
Fig. 5.2
Direct (Non disguised)
Indirect (Disguised)
Focus Groups Depth Interviews
Projective Techniques
Qualitative Research Procedures
4-11
Definition of Projective Techniques
An unstructured, indirect form of questioning that encourages respondents to project their underlying motivations, beliefs, attitudes or feelings regarding the issues of concern. In projective techniques, respondents are asked to interpret the behavior of others. In interpreting the behavior of others, respondents indirectly project their own motivations, beliefs, attitudes, or feelings into the situation.
4-12
Word AssociationIn word association, respondents are presented with a list of words, one at a time and asked to respond to each with the first word that comes to mind. The words of interest, called test words, are interspersed throughout the list which also contains some neutral, or filler words to disguise the purpose of the study. Responses are analyzed by calculating:
(1) the frequency with which any word is given as a response; (2) the amount of time that elapses before a response is given; and (3) the number of respondents who do not respond at all to a test word within a reasonable period of time.
4-13
Completion Techniques
In Sentence completion, respondents are given incomplete sentences and asked to complete them. Generally, they are asked to use the first word or phrase that comes to mind.
A person who shops at Sears is ______________________
A person who receives a gift certificate good for Sak's Fifth Avenue would be __________________________________
J. C. Penney is most liked by _________________________
When I think of shopping in a department store, I ________
A variation of sentence completion is paragraph completion, in which the respondent completes a paragraph beginning with the stimulus phrase.
4-14
Completion Techniques
In story completion, respondents are given part of a story – enough to direct attention to a particular topic but not to hint at the ending. They are required to give the conclusion in their own words.
4-15
Construction Techniques
With a picture response, the respondents are asked to describe a series of pictures of ordinary as well as unusual events. The respondent's interpretation of the pictures gives indications of that individual's personality.
In cartoon tests, cartoon characters are shown in a specific situation related to the problem. The respondents are asked to indicate what one cartoon character might say in response to the comments of another character. Cartoon tests are simpler to administer and analyze than picture response techniques.
4-16
A Cartoon Test
Let’s see if we can pick up some
house wares at Sears
Figure 5.4
SearsSears
4-17
Expressive Techniques
In expressive techniques, respondents are presented with a verbal or visual situation and asked to relate the feelings and attitudes of other people to the situation.
Role playing Respondents are asked to play the role or assume the behavior of someone else.
Third-person technique The respondent is presented with a verbal or visual situation and the respondent is asked to relate the beliefs and attitudes of a third person rather than directly expressing personal beliefs and attitudes. This third person may be a friend, neighbor, colleague, or a “typical” person.
4-18
Advantages of Projective Techniques
They may elicit responses that subjects would be unwilling or unable to give if they knew the purpose of the study.
Helpful when the issues to be addressed are personal, sensitive, or subject to strong social norms.
Helpful when underlying motivations, beliefs, and attitudes are operating at a subconscious level.
4-19
A Classification of Survey Methods
Traditional Telephone
Computer-Assisted Telephone Interviewing
Mail Interview
Mail Panel
Fig. 6.1
In-Home Mall Intercept
Computer-Assisted Personal
Interviewing
E-mail Internet
Survey Methods
Telephone Personal Mail Electronic
4-20Observation Methods Structured versus Unstructured Observation
For structured observation, the researcher specifies in detail what is to be observed and how the measurements are to be recorded, e.g., an auditor performing inventory analysis in a store.
In unstructured observation, the observer monitors all aspects of the phenomenon that seem relevant to the problem at hand, e.g., observing children playing with new toys.
4-21Observation Methods Disguised versus Undisguised Observation
In disguised observation, the respondents are unaware that they are being observed. Disguise may be accomplished by using one-way mirrors, hidden cameras, or inconspicuous mechanical devices. Observers may be disguised as shoppers or sales clerks.
In undisguised observation, the respondents are aware that they are under observation.
4-22Observation Methods Natural versus Contrived Observation
Natural observation involves observing behavior as it takes places in the environment. For example, one could observe the behavior of respondents eating fast food in Burger King.
In contrived observation, respondents' behavior is observed in an artificial environment, such as a test kitchen.
4-23
A Classification of Observation Methods
Observation Methods
Personal Observation
Mechanical Observation
Trace Analysis
Content Analysis
Audit
Fig. 6.3
Classifying
Observation
Methods
4-24
Concept of Causality
A statement such as "X causes Y " will have thefollowing meaning to an ordinary person and to ascientist.
____________________________________________________Ordinary Meaning Scientific Meaning
____________________________________________________X is the only cause of Y. X is only one of a number of
possible causes of Y.
X must always lead to Y The occurrence of X makes the (X is a deterministic occurrence of Y more probablecause of Y). (X is a probabilistic cause of Y).
It is possible to prove We can never prove that X is athat X is a cause of Y. cause of Y. At best, we can
infer that X is a cause of Y.
4-25
Definitions and Concepts
Independent variables are variables or alternatives that are manipulated and whose effects are measured and compared, e.g., price levels. Test units are individuals, organizations, or other entities whose response to the independent variables or treatments is being examined, e.g., consumers or stores. Dependent variables are the variables which measure the effect of the independent variables on the test units, e.g., sales, profits, and market shares. Extraneous variables are all variables other than the independent variables that affect the response of the test units, e.g., store size, store location, and competitive effort.
4-26
Experimental Design
An experimental design is a set of procedures specifying
the test units and how these units are to be divided into homogeneous subsamples, what independent variables or treatments are to be manipulated, what dependent variables are to be measured, and how the extraneous variables are to be controlled.
4-27
Validity in Experimentation
Internal validity refers to whether the manipulation of the independent variables or treatments actually caused the observed effects on the dependent variables. Control of extraneous variables is a necessary condition for establishing internal validity.External validity refers to whether the cause-and-effect relationships found in the experiment can be generalized. To what populations, settings, times, independent variables and dependent variables can the results be projected?
4-28
Controlling Extraneous Variables
Randomization refers to the random assignment of test units to experimental groups by using random numbers. Treatment conditions are also randomly assigned to experimental groups.Matching involves comparing test units on a set of key background variables before assigning them to the treatment conditions. Statistical control involves measuring the extraneous variables and adjusting for their effects through statistical analysis.Design control involves the use of experiments designed to control specific extraneous variables.
4-29
A Classification of Experimental Designs
Pre-experimental
One-Shot Case Study
One Group Pretest-Posttest
Static Group
True Experimental
Pretest-Posttest Control Group
Posttest: Only Control Group
Solomon Four- Group
Quasi Experimental
Time Series
Multiple Time Series
Statistical
Randomized Blocks
Latin Square
Factorial Design
Figure 7.1
Experimental Designs
4-30
Factorial Design
Is used to measure the effects of two or more independent variables at various levels. A factorial design may also be conceptualized as a table. In a two-factor design, each level of one variable represents a row and each level of another variable represents a column.
4-31
Competition
Overall Marketing Strategy
Soci
o-C
ult
ura
l En
viro
nm
ent
Nee
d fo
r Se
crec
y
New Product DevelopmentResearch on Existing ProductsResearch on other Elements
Simulated Test Marketing
Controlled Test Marketing
Standard Test Marketing
National Introduction
Stop
and
Ree
valu
ate
-ve
-ve
-ve
-ve
Very +veOther Factors
Very +veOther Factors
Very +veOther Factors
Selecting a Test-Marketing Strategy
4-32
Criteria for the Selection of Test Markets
Test Markets should have the following qualities:1) Be large enough to produce meaningful projections. They
should contain at least 2% of the potential actual population.2) Be representative demographically.3) Be representative with respect to product consumption behavior.4) Be representative with respect to media usage.5) Be representative with respect to competition.6) Be relatively isolated in terms of media and physical distribution.7) Have normal historical development in the product class8) Have marketing research and auditing services available9) Not be over-tested
4-33
Measurement and Scaling
Measurement means assigning numbers or other symbols to characteristics of objects according to certain prespecified rules.
One-to-one correspondence between the numbers and the characteristics being measured. The rules for assigning numbers should be standardized and applied uniformly. Rules must not change over objects or time.
4-34
Measurement and Scaling
Scaling involves creating a continuum upon which measured objects are located.
Consider an attitude scale from 1 to 100. Each respondent is assigned a number from 1 to 100, with 1 = Extremely Unfavorable, and 100 = Extremely Favorable. Measurement is the actual assignment of a number from 1 to 100 to each respondent. Scaling is the process of placing the respondents on a continuum with respect to their attitude toward department stores.
4-35
7 38
Primary Scales of MeasurementScaleNominal Numbers
Assignedto Runners
Ordinal Rank Orderof Winners
Interval PerformanceRating on a0 to 10 Scale
Ratio Time to Finish, in Seconds
Figure 8.1
Thirdplace
Secondplace
Firstplace
Finish
Finish
8.2 9.1 9.6
15.2 14.1 13.4
4-36
A Classification of Scaling Techniques
Likert Semantic Differential
Stapel
Figure 8.2
Scaling Techniques
NoncomparativeScales
Comparative Scales
Paired Comparison
Rank Order
Constant Sum
Q-Sort and Other Procedures
Continuous Rating Scales
Itemized Rating Scales
4-37
A Comparison of Scaling Techniques
Comparative scales involve the direct comparison of stimulus objects. Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties.
In noncomparative scales, each object is scaled independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ratio scaled.
4-38
Brand Rank Order
1. Crest _________
2. Colgate _________
3. Aim _________
4. Gleem _________
5. Macleans _________
6. Ultra Brite _________
7. Close Up _________
8. Pepsodent _________
9. Plus White _________
10. Stripe _________
Preference for Toothpaste Brands Using Rank Order ScalingFigure 8.4 cont.
Form
4-39
Figure 8.5 cont.
FormAverage Responses of Three Segments
Attribute Segment I Segment II Segment III1. Mildness2. Lather 3. Shrinkage 4. Price 5. Fragrance 6. Packaging 7. Moisturizing 8. Cleaning Power
Sum
8 2 42 4 173 9 7
53 17 99 0 197 5 95 3 20
13 60 15100 100 100
Importance of Bathing Soap Attributes Using a Constant Sum Scale
4-40
Noncomparative Scaling Techniques
Respondents evaluate only one object at a time, and for this reason noncomparative scales are often referred to as monadic scales. Noncomparative techniques consist of continuous and itemized rating scales.
4-41
Likert ScaleThe Likert scale requires the respondents to indicate a degree of agreement ordisagreement with each of a series of statements about the stimulus objects.
Strongly Disagree Neither Agree Strongly disagree agree nor agree
disagree
1. Sears sells high quality merchandise. 1 2X 3 4 5
2. Sears has poor in-store service. 1 2X 3 4 5
3. I like to shop at Sears. 1 2 3X 4 5
The analysis can be conducted on an item-by-item basis (profile analysis), or a total (summated) score can be calculated.
When arriving at a total score, the categories assigned to the negative statements by the respondents should be scored by reversing the scale.
4-42
Semantic Differential ScaleThe semantic differential is a seven-point rating scale with end points associated with bipolar labels that have semantic meaning.
SEARS IS:Powerful --:--:--:--:-X-:--:--: WeakUnreliable --:--:--:--:--:-X-:--: ReliableModern --:--:--:--:--:--:-X-: Old-fashioned
The negative adjective or phrase sometimes appears at the left side of the scale and sometimes at the right. This controls the tendency of some respondents, particularly those with very positive or very negative attitudes, to mark theright- or left-hand sides without reading the labels. Individual items on a semantic differential scale may be scored on either a -3 to +3 or a 1 to 7 scale.
4-43
A Semantic Differential Scale for Measuring Self- Concepts, Person Concepts, and Product Concepts
1) Rugged :---:---:---:---:---:---:---: Delicate 2) Excitable :---:---:---:---:---:---:---: Calm3) Uncomfortable :---:---:---:---:---:---:---: Comfortable4) Dominating :---:---:---:---:---:---:---: Submissive5) Thrifty :---:---:---:---:---:---:---: Indulgent6) Pleasant :---:---:---:---:---:---:---: Unpleasant7) Contemporary :---:---:---:---:---:---:---: Obsolete8) Organized :---:---:---:---:---:---:---: Unorganized9) Rational :---:---:---:---:---:---:---: Emotional
10) Youthful :---:---:---:---:---:---:---: Mature11) Formal :---:---:---:---:---:---:---: Informal12) Orthodox :---:---:---:---:---:---:---: Liberal13) Complex :---:---:---:---:---:---:---: Simple14) Colorless :---:---:---:---:---:---:---: Colorful15) Modest :---:---:---:---:---:---:---: Vain
4-44
Stapel ScaleThe Stapel scale is a unipolar rating scale with ten categoriesnumbered from -5 to +5, without a neutral point (zero). This scaleis usually presented vertically.
SEARS
+5 +5+4 +4+3 +3+2 +2X+1 +1
HIGH QUALITY POOR SERVICE-1 -1-2 -2-3 -3-4X -4-5 -5
The data obtained by using a Stapel scale can be analyzed in thesame way as semantic differential data.
4-45
Thermometer ScaleInstructions: Please indicate how much you like McDonald’s hamburgers by coloring in the thermometer. Start at the bottom and color up to the temperature level that best indicates how strong your preference is. Form:
Smiling Face Scale Instructions: Please point to the face that shows how much you like the Barbie Doll. If you do not like the Barbie Doll at all, you would point to Face 1. If you liked it very much, you would point to Face 5. Form:
1 2 3 4 5
Figure 9.3
Like very much
Dislike very much
100 75 50 25 0
Some Unique Rating Scale Configurations
4-46
Validity
Construct validity addresses the question of what construct or characteristic the scale is, in fact, measuring. Construct validity includes convergent, discriminant, and nomological validity.Convergent validity is the extent to which the scale correlates positively with other measures of the same construct. Discriminant validity is the extent to which a measure does not correlate with other constructs from which it is supposed to differ.Nomological validity is the extent to which the scale correlates in theoretically predicted ways with measures of different but related constructs.
4-47
Questionnaire Definition
A questionnaire is a formalized set of questions for obtaining information from respondents.
4-48
Specify the Information Needed
Design the Question to Overcome the Respondent’s Inability and Unwillingness to Answer
Determine the Content of Individual Questions
Decide the Question Structure
Determine the Question Wording
Arrange the Questions in Proper Order
Reproduce the Questionnaire
Specify the Type of Interviewing Method
Identify the Form and Layout
Eliminate Bugs by Pre-testing
Fig. 10.1
Questionnaire Design Process
4-49Choosing Question Structure Unstructured Questions
Unstructured questions are open-ended questions that respondents answer in their own words.
Do you intend to buy a new car within the next six months?
__________________________________
4-50Choosing Question Structure Structured Questions
Structured questions specify the set of response alternatives and the response format. A structured question may be multiple-choice, dichotomous, or a scale.
4-51Choosing Question Structure Multiple-Choice Questions
In multiple-choice questions, the researcher provides a choice of answers and respondents are asked to select one or more of the alternatives given.
Do you intend to buy a new car within the next six months?____ Definitely will not buy____ Probably will not buy____ Undecided____ Probably will buy____ Definitely will buy____ Other (please specify)
4-52Choosing Question Structure Dichotomous Questions
A dichotomous question has only two response alternatives: yes or no, agree or disagree, and so on. Often, the two alternatives of interest are supplemented by a neutral alternative, such as “no opinion,” “don't know,” “both,” or “none.”
Do you intend to buy a new car within the next six months?
_____ Yes _____ No _____ Don't know
4-53Choosing Question Wording Use Ordinary Words
“Do you think the distribution of soft drinks is adequate?” (Incorrect)
“Do you think soft drinks are readily available when you want to buy them?” (Correct)
4-54Choosing Question Wording Use Unambiguous Words
In a typical month, how often do you shop in department stores? _____ Never _____ Occasionally _____ Sometimes _____ Often _____ Regularly (Incorrect)
In a typical month, how often do you shop in department stores? _____ Less than once _____ 1 or 2 times _____ 3 or 4 times _____ More than 4 times (Correct)
4-55
Ownership of Store, Bank, and Other Charge Cards
Introduction
Store Charge
Card
Purchased Products in a Specific Department Store during the Last Two Months
How was Payment made? Ever Purchased in a Department Store?
Bank Charge
Card
Other Charge
Card
Intentions to Use Store, Bank, and other Charge Cards
Yes
Yes
No
No
CashCreditOther
Fig. 10.2
Flow Chart for Questionnaire Design
4-56
Pretesting
Pretesting refers to the testing of the questionnaire on a small sample of respondents to identify and eliminate potential problems.
A questionnaire should not be used in the field survey without adequate pretesting. All aspects of the questionnaire should be tested, including question content, wording, sequence, form and layout, question difficulty, and instructions. The respondents for the pretest and for the actual survey should be drawn from the same population. Pretests are best done by personal interviews, even if the actual survey is to be conducted by mail, telephone, or electronic means, because interviewers can observe respondents' reactions and attitudes.
4-57
Observational Forms
Department Store ProjectWho: Purchasers, browsers, males, females, parents with children, or children alone.What: Products/brands considered, products/brands purchased, size, price of package inspected, or influence of children or other family members.When: Day, hour, date of observation.Where: Inside the store, checkout counter, or type of department within the store.Why: Influence of price, brand name, package size, promotion, or family members on the purchase.Way: Personal observer disguised as sales clerk, undisguised personal observer, hidden camera, or obtrusive mechanical device.
4-58
Step 1. Specify The Information Needed
Step 2. Type of Interviewing Method
Step 3. Individual Question Content
Step 4. Overcome Inability and Unwillingness to Answer
Step 5. Choose Question Structure
Step 6. Choose Question Wording
Step 7. Determine the Order of Questions
Step 8. Form and Layout
Step 9. Reproduce the Questionnaire
Step 10. Pretest
Table 10.1
Questionnaire Design Checklist
4-59
Sample vs. CensusTable 11.1
Conditions Favoring the Use of Type of Study
Sample Census
1. Budget
Small
Large
2. Time available
Short Long
3. Population size
Large Small
4. Variance in the characteristic
Small Large
5. Cost of sampling errors
Low High
6. Cost of nonsampling errors
High Low
7. Nature of measurement
Destructive Nondestructive
8. Attention to individual cases Yes No
4-60
The Sampling Design ProcessFig. 11.1
Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process
4-61
Define the Target Population
The target population is the collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made. The target population should be defined in terms of elements, sampling units, extent, and time.
An element is the object about which or from which the information is desired, e.g., the respondent. A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process. Extent refers to the geographical boundaries.Time is the time period under consideration.
4-62Sample Sizes Used in Marketing Research Studies
Table 11.2
Type of Study
Minimum Size Typical Range
Problem identification research (e.g. market potential)
500
1,000-2,500
Problem-solving research (e.g. pricing)
200 300-500
Product tests
200 300-500
Test marketing studies
200 300-500
TV, radio, or print advertising (per commercial or ad tested)
150 200-300
Test-market audits
10 stores 10-20 stores
Focus groups
2 groups 4-12 groups
4-63
Classification of Sampling TechniquesFig. 11.2
Sampling Techniques
NonprobabilitySampling Techniques
ProbabilitySampling Techniques
ConvenienceSampling
JudgmentalSampling
QuotaSampling
SnowballSampling
SystematicSampling
StratifiedSampling
ClusterSampling
Other SamplingTechniques
Simple RandomSampling
4-64
Data Preparation ProcessFig. 14.1
Select Data Analysis Strategy
Prepare Preliminary Plan of Data Analysis
Check Questionnaire
Edit
Code
Transcribe
Clean Data
Statistically Adjust the Data
4-65
Selecting a Data Analysis Strategy
Earlier Steps (1, 2, & 3) of the Marketing Research Process
Known Characteristics of the Data
Data Analysis Strategy
Properties of Statistical Techniques
Background and Philosophy of the Researcher
Fig. 14.5
4-66
A Classification of Univariate TechniquesFig. 14.6
Independent Related
Independent Related* Two- Group test
* Z test* One-Way
ANOVA
* Pairedt test
* Chi-Square* Mann-Whitney* Median* K-S* K-W ANOVA
* Sign* Wilcoxon* McNemar* Chi-Square
Metric Data Non-numeric Data
Univariate Techniques
One Sample Two or More Samples
One Sample Two or More Samples
* t test* Z test
* Frequency* Chi-Square* K-S* Runs* Binomial
4-67
A Classification of Multivariate TechniquesFig. 14.7
More Than One Dependent
Variable* Multivariate
Analysis of Variance and Covariance
* Canonical Correlation
* Multiple Discriminant Analysis
* Cross- Tabulation
* Analysis of Variance and Covariance
* Multiple Regression
* Conjoint Analysis
* Factor Analysis
One Dependent Variable
Variable Interdependence
Interobject Similarity
* Cluster Analysis* Multidimensional
Scaling
Dependence Technique
Interdependence Technique
Multivariate Techniques
4-68
Frequency Distribution
In a frequency distribution, one variable is considered at a time. A frequency distribution for a variable produces a table of frequency counts, percentages, and cumulative percentages for all the values associated with that variable.
4-69
The mean, or average value, is the most commonly used measure of central tendency. The mean, ,is given by
Where,Xi = Observed values of the variable Xn = Number of observations (sample size)
The mode is the value that occurs most frequently. It represents the highest peak of the distribution. The mode is a good measure of location when the variable is inherently categorical or has otherwise been grouped into categories.
Statistics Associated with Frequency Distribution Measures of Location
X = X i/nΣi=1
nX
4-70
The median of a sample is the middle value when the data are arranged in ascending or descending order. If the number of data points is even, the median is usually estimated as the midpoint between the two middle values – by adding the two middle values and dividing their sum by 2. The median is the 50th percentile.
Statistics Associated with Frequency Distribution Measures of Location
4-71
The range measures the spread of the data. It is simply the difference between the largest and smallest values in the sample. Range = Xlargest –Xsmallest.
The interquartile range is the difference between the 75th and 25th percentile. For a set of data points arranged in order of magnitude, the pth
percentile is the value that has p% of the data points below it and (100 - p)% above it.
Statistics Associated with Frequency Distribution Measures of Variability
4-72
The variance is the mean squared deviation from the mean. The variance can never be negative. The standard deviation is the square root of the variance.
The coefficient of variation is the ratio of the standard deviation to the mean expressed as a percentage, and is a unitless measure of relative variability.
sx = (Xi - X)2
n - 1Σi =1
n
CV = sx/X
Statistics Associated with Frequency Distribution Measures of Variability
4-73
Skewness. The tendency of the deviations from the mean to be larger in one direction than in the other. It can be thought of as the tendency for one tail of the distribution to be heavier than the other.
Kurtosis is a measure of the relative peakedness 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 that the distribution is flatter than a normal distribution.
Statistics Associated with Frequency Distribution Measures of Shape
4-74
Skewness of a DistributionFigure 15.2
Skewed Distribution
Symmetric Distribution
Mean Median Mode (a)
Mean Median Mode (b)
4-75
Steps Involved in Hypothesis TestingFig. 15.3
Draw Marketing Research Conclusion
Formulate H0 and H1
Select Appropriate Test
Choose Level of Significance
Determine Probability Associated with Test
Statistic
Determine Critical Value of Test Statistic TSCR
Determine if TSCR falls into (Non)
Rejection Region
Compare with Level of Significance, α
Reject or Do not Reject H0
Collect Data and Calculate Test Statistic
4-76
A Broad Classification of Hypothesis Tests
Median/ RankingsDistributions Means Proportions
Figure 15.6
Tests of Association
Tests of Differences
Hypothesis Tests
4-77
Cross-Tabulation
While a frequency distribution describes one variable at a time, a cross-tabulation describes two or more variables simultaneously. Cross-tabulation results in tables that reflect the joint distribution of two or more variables with a limited number of categories or distinct values, e.g., Table 15.3.
4-78
Gender and Internet UsageTable 15.3
Gender Row Internet Usage Male Female Total Light (1) 5 10 15 Heavy (2) 10 5 15 Column Total 15 15
4-79
Internet Usage by GenderTable 15.4
Gender Internet Usage Male Female Light 33.3% 66.7% Heavy 66.7% 33.3% Column total 100% 100%
4-80
Gender by Internet UsageTable 15.5
Internet Usage Gender Light Heavy Total Male 33.3% 66.7% 100.0% Female 66.7% 33.3% 100.0%
4-81
Refined Association between the Two
Variables
No Association between the Two
Variables
No Change in the Initial Pattern
Some Association between the Two
Variables
Introduction of a Third Variable in Cross- TabulationFig. 15.7
Some Association between the Two
Variables
No Association between the Two
Variables
Introduce a Third Variable
Introduce a Third Variable
Original Two Variables
4-82
Purchase of Fashion Clothing by Marital StatusTable 15.6
Purchase of Fashion
Current Marital Status
Clothing Married Unmarried
High 31% 52%
Low 69% 48%
Column 100% 100%
Number of respondents
700 300
4-83
Purchase of Fashion Clothing by Marital StatusTable 15.7
Purchase ofFashion
SexMale Female
Clothing Marr ied NotMarr ied
Marr ied NotMarr ied
High 35% 40% 25% 60%
Low 65% 60% 75% 40%
Columntotals
100% 100% 100% 100%
Number ofcases
400 120 300 180
4-84Eating Frequently in Fast-Food Restaurants by Family SizeTable 15.12
Eat Frequently in Fast-Food Restaurants
Family Size
Small Large
Yes 65% 65%
No 35% 35%
Column totals 100% 100%
Number of cases 500 500
4-85
Small Large Small LargeYes 65% 65% 65% 65%No 35% 35% 35% 35%Column totals 100% 100% 100% 100%Number of respondents 250 250 250 250
IncomeEat Frequently in Fast-
Food RestaurantsFamily size Family size
Low High
Eating Frequently in Fast Food-Restaurants by Family Size & IncomeTable 15.13
4-86
Chi-square DistributionFigure 15.8
Reject H0
Do Not Reject H0
CriticalValue
χ
2
4-87Statistics Associated with Cross-Tabulation Chi-Square
The chi-square statistic ( ) is used to test the statistical significance of the observed association in a cross-tabulation. The expected frequency for each cell can be calculated by using a simple formula:
χ2
fe = nrncn
where nr = total number in the rownc = total number in the columnn = total sample size
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For the data in Table 15.3, the expected frequencies forthe cells going from left to right and from top tobottom, are:
Then the value of is calculated as follows:
15 X 1530 = 7.50 15 X 15
30 = 7.50
15 X 1530 = 7.50 15 X 15
30 = 7.50
χ2 = (fo - fe)2
feΣall
cells
χ2
Statistics Associated with Cross-Tabulation Chi-Square
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For the data in Table 15.3, the value of is
calculated as:
= (5 -7.5)2 + (10 - 7.5)2 + (10 - 7.5)2 + (5 - 7.5)2
7.5 7.5 7.5 7.5
=0.833 + 0.833 + 0.833+ 0.833
= 3.333
χ2
Statistics Associated with Cross-Tabulation Chi-Square
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Asymmetric lambda measures the percentage improvement in predicting the value of the dependent variable, given the value of the independent variable. Lambda also varies between 0 and 1. A value of 0 means no improvement in prediction. A value of 1 indicates that the prediction can be made without error. This happens when each independent variable category is associated with a single category of the dependent variable.Asymmetric lambda is computed for each of the variables (treating it as the dependent variable). A symmetric lambda is also computed, which is a kind of average of the two asymmetric values. 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.
Statistics Associated with Cross-Tabulation Lambda Coefficient
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Independent Samples
Paired Samples Independent
SamplesPaired
Samples* Two-Group t test
* Z test
* Pairedt test * Chi-Square
* Mann-Whitney* Median* K-S
* Sign* Wilcoxon* McNemar* Chi-Square
A Classification of Hypothesis Testing Procedures for Examining DifferencesFig. 15.9 Hypothesis Tests
One Sample Two or More Samples
One Sample Two or More Samples
* t test* Z test
* Chi-Square * K-S * Runs* Binomial
Parametric Tests (Metric Tests)
Non-parametric Tests (Nonmetric Tests)
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Non-Parametric Tests
Nonparametric tests are used when the independent variables are nonmetric. Like parametric tests, nonparametric tests are available for testing variables from one sample, two independent samples, or two related samples.
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Sometimes the researcher wants to test whether theobservations for a particular variable could reasonablyhave come from a particular distribution, such as thenormal, uniform, or Poisson distribution.
The Kolmogorov-Smirnov (K-S) one-sample testis one such goodness-of-fit test. The K-S compares thecumulative distribution function for a variable with aspecified distribution. Ai denotes the cumulativerelative frequency for each category of the theoretical(assumed) distribution, and Oi the comparable value ofthe sample frequency. The K-S test is based on themaximum value of the absolute difference between Aiand Oi . The test statistic is
Non-Parametric Tests One Sample
K = Max Ai - Oi
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The chi-square test can also be performed on a single variable from one sample. In this context, the chi-square serves as a goodness-of-fit test. The runs test is a test of randomness for the dichotomous variables. This test is conducted by determining whether the order or sequence in which observations are obtained is random. The binomial test is also a goodness-of-fit 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.
Non-Parametric Tests One Sample
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When the difference in the location of two populations is to be compared based on observations from two independent samples, and the variable is measured on an ordinal scale, the Mann-Whitney U test can be used. In the Mann-Whitney U test, the two samples are combined and the cases are ranked in order of increasing size. The test statistic, U, is computed as the number of times a score from sample or group 1 precedes a score from group 2. If the samples are from the same population, the distribution ofscores from the two groups in the rank list should be random. An extreme value of U would indicate a nonrandom pattern, pointing to the inequality of the two groups. For samples of less than 30, the exact significance level for U is computed. For larger samples, U is transformed into a normally distributed z statistic. This z can be corrected for ties within ranks.
Non-Parametric Tests Two Independent Samples
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SPSS Windows
The main program in SPSS is FREQUENCIES. It produces a table of frequency counts, percentages, and cumulative percentages for the values of each variable. It gives all of the associated statistics. If the data are interval scaled and only the summary statistics are desired, the DESCRIPTIVES procedure can be used. The EXPLORE procedure produces summary statistics and graphical displays, either for all of the cases or separately for groups of cases. Mean, median, variance, standard deviation, minimum, maximum, and range are some of the statistics that can be calculated.
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SPSS WindowsTo select these procedures click:
Analyze>Descriptive Statistics>FrequenciesAnalyze>Descriptive Statistics>DescriptivesAnalyze>Descriptive Statistics>Explore
The major cross-tabulation program is CROSSTABS.This program will display the cross-classification tablesand provide cell counts, row and column percentages,the chi-square test for significance, and all themeasures of the strength of the association that havebeen discussed.
To select these procedures click:
Analyze>Descriptive Statistics>Crosstabs
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The major program for conducting parametrictests in SPSS is COMPARE MEANS. This program canbe used to conduct t tests on one sample orindependent or paired samples. To select theseprocedures using SPSS for Windows click:
Analyze>Compare Means>Means …Analyze>Compare Means>One-Sample T Test …Analyze>Compare Means>Independent-
Samples T Test …Analyze>Compare Means>Paired-Samples T
Test …
SPSS Windows
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The nonparametric tests discussed in this chapter canbe conducted using NONPARAMETRIC TESTS.
To select these procedures using SPSS for Windowsclick:
Analyze>Nonparametric Tests>Chi-Square …Analyze>Nonparametric Tests>Binomial …Analyze>Nonparametric Tests>Runs …Analyze>Nonparametric Tests>1-Sample K-S …Analyze>Nonparametric Tests>2 Independent
Samples …Analyze>Nonparametric Tests>2 Related
Samples …
SPSS Windows
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Product Moment Correlation
The product moment correlation, r, summarizes the strength of association between two metric (interval or ratio scaled) variables, say X and Y. It is an index used to determine whether a linear or straight-line relationship exists between X and Y. As it was originally proposed by Karl Pearson, it is also known as the Pearson correlation coefficient. It is also referred to as simple correlation, bivariate correlation, or merely the correlation coefficient.
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Product Moment Correlation
r varies between -1.0 and +1.0. The correlation coefficient between two variables will be the same regardless of their underlying units of measurement.
4-102Statistics Associated with Bivariate Regression Analysis
Regression coefficient. The estimated parameter b is usually referred to as the non-standardized regression coefficient.
Scattergram. A scatter diagram, or scattergram, is a plot of the values of two variables for all the cases or observations.
Standard error of estimate. This statistic, SEE, is the standard deviation of the actual Y values from the predicted values.
Standard error. The standard deviation of b, SEb, is called the standard error.
Y
4-103Statistics Associated with Bivariate Regression Analysis
Standardized regression coefficient. Also termed the beta coefficient or beta weight, this is the slope obtained by the regression of Y on Xwhen the data are standardized.
Sum of squared errors. The distances of all the points from the regression line are squared and added together to arrive at the sum of squared errors, which is a measure of total error, .
t statistic. A t statistic with n - 2 degrees of freedom can be used to test the null hypothesis that no linear relationship exists between X and Y, or H0: = 0, where t = b
SEb β 1
Σe j2
4-104Conducting Bivariate Regression Analysis Plot the Scatter Diagram
A scatter diagram, or scattergram, is a plot of the values of two variables for all the cases or observations. The most commonly used technique for fitting a straight line to a scattergram is the least-squares procedure.
In fitting the line, the least-squares procedure minimizes the sum of squared errors, . Σe j
2
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Conducting Bivariate Regression AnalysisFig. 17.2
Plot the Scatter Diagram
Formulate the General Model
Estimate the Parameters
Estimate Standardized Regression Coefficients
Test for Significance
Determine the Strength and Significance of Association
Check Prediction Accuracy
Examine the Residuals
Cross-Validate the Model
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Multiple Regression
The general form of the multiple regression modelis as follows:
which is estimated by the following equation:
= a + b1X1 + b2X2 + b3X3 + . . . + bkXk
As before, the coefficient a represents the intercept,but the b's are now the partial regression coefficients.
Y = β 0 + β 1X1 + β 2X2 + β 3 X3+ . . . + β k Xk + e
Y
e
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MulticollinearityMulticollinearity arises when intercorrelations among the predictors are very high. Multicollinearity can result in several problems, including:
The partial regression coefficients may not be estimated precisely. The standard errors are likely to be high.The magnitudes as well as the signs of the partial regression coefficients may change from sample to sample.It becomes difficult to assess the relative importance of the independent variables in explaining the variation in the dependent variable. Predictor variables may be incorrectly included or removed in stepwise regression.
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SPSS WindowsThe CORRELATE program computes Pearson product moment correlationsand partial correlations with significance levels. Univariate statistics,covariance, and cross-product deviations may also be requested.Significance levels are included in the output. To select these proceduresusing SPSS for Windows click:
Analyze>Correlate>Bivariate …
Analyze>Correlate>Partial …
Scatterplots can be obtained by clicking:
Graphs>Scatter …>Simple>Define
REGRESSION calculates bivariate and multiple regression equations,associated statistics, and plots. It allows for an easy examination ofresiduals. This procedure can be run by clicking:
Analyze>Regression Linear …
4-109Similarities and Differences between ANOVA, Regression, and Discriminant Analysis
ANOVA REGRESSION DISCRIMINANT ANALYSIS
SimilaritiesNumber of One One OnedependentvariablesNumber ofindependent Multiple Multiple Multiplevariables
DifferencesNature of thedependent Metric Metric CategoricalvariablesNature of theindependent Categorical Metric Metricvariables
Table 18.1
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Discriminant AnalysisDiscriminant analysis is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature.
The objectives of discriminant analysis are as follows:Development of discriminant functions, or linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups).Examination of whether significant differences exist among the groups, in terms of the predictor variables.Determination of which predictor variables contribute to most of the intergroup differences.Classification of cases to one of the groups based on the values of the predictor variables.Evaluation of the accuracy of classification.
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Canonical correlation. Canonical correlation measures the extent of association between the discriminant scores and the groups. It is a measure of association between the single discriminant function and the set of dummy variables that define the group membership.Centroid. The centroid is the mean values for the discriminant scores for a particular group. There are as many centroids as there are groups, as there is one for each group. The means for a group on all the functions are the group centroids. Classification matrix. Sometimes also called confusion or prediction matrix, the classification matrix contains the number of correctly classified and misclassified cases.
Statistics Associated with Discriminant Analysis
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Discriminant function coefficients. The discriminant function coefficients (unstandardized) are the multipliers of variables, when the variables are in the original units of measurement. Discriminant scores. The unstandardized coefficients are multiplied by the values of the variables. These products are summed and added to the constant term to obtain the discriminant scores.Eigenvalue. For each discriminant function, the Eigenvalue is the ratio of between-group to within-group sums of squares. Large Eigenvalues imply superior functions.
Statistics Associated with Discriminant Analysis
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Conducting Discriminant AnalysisFig. 18.1
Assess Validity of Discriminant Analysis
Estimate the Discriminant Function Coefficients
Determine the Significance of the Discriminant Function
Formulate the Problem
Interpret the Results
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SPSS Windows
The DISCRIMINANT program performs both two- group and multiple discriminant analysis. To select this procedure using SPSS for Windows click:
Analyze>Classify>Discriminant …
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Factor AnalysisFactor analysis is a general name denoting a class of procedures primarily used for data reduction and summarization. Factor analysis is an interdependence technique in that an entire set of interdependent relationships is examined without making the distinction between dependent and independent variables.Factor analysis is used in the following circumstances:
To identify underlying dimensions, or factors, that explain the correlations among a set of variables. To identify a new, smaller, set of uncorrelated variables to replace the original set of correlated variables in subsequent multivariate analysis (regression or discriminant analysis). To identify a smaller set of salient variables from a larger setfor use in subsequent multivariate analysis.
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It is possible to select weights or factor score coefficients so that the first factor explains the largest portion of the total variance. Then a second set of weights can be selected, so that the second factor accounts for most of the residual variance, subject to being uncorrelated with the first factor. This same principle could be applied to selecting additional weights for the additional factors.
Factor Analysis Model
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Conducting Factor AnalysisFig 19.1
Construction of the Correlation Matrix
Method of Factor Analysis
Determination of Number of Factors
Determination of Model Fit
Problem formulation
Calculation ofFactor Scores
Interpretation of Factors
Rotation of Factors
Selection ofSurrogate Variables
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A Priori Determination. Sometimes, because of prior knowledge, the researcher knows how many factors to expect and thus can specify the number of factors to be extracted beforehand.
Determination Based on Eigenvalues. In this approach, only factors with Eigenvalues greater than 1.0 are retained. An Eigenvalue represents the amount of variance associated with the factor. Hence, only factors with a variance greater than 1.0 are included. Factors with variance less than 1.0 are no better than a single variable, since, due to standardization, each variable has a variance of 1.0. If the number of variables is less than 20, this approach will result in a conservative number of factors.
Conducting Factor Analysis Determine the Number of Factors
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SPSS Windows
To select this procedures using SPSS for Windows click:
Analyze>Data Reduction>Factor …
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Cluster Analysis
Cluster analysis is a class of techniques used to classify objects or cases into relatively homogeneous groups called clusters. Objects in each cluster tend to be similar to each other and dissimilar to objects in the other clusters. Cluster analysis is also called classification analysis, or numerical taxonomy. Both cluster analysis and discriminant analysis are concerned with classification. However, discriminant analysis requires prior knowledge of the cluster or group membership for each object or case included, to develop the classification rule. In contrast, in cluster analysis there is no a priori information about the group or cluster membership for any of the objects. Groups or clusters are suggested by the data, not defined a priori.
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An Ideal Clustering Situation
Variable 2
Varia
ble
1
Fig. 20.1
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Conducting Cluster Analysis
Formulate the Problem
Assess the Validity of Clustering
Select a Distance Measure
Select a Clustering Procedure
Decide on the Number of Clusters
Interpret and Profile Clusters
Fig. 20.3
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A Classification of Clustering Procedures
SequentialThreshold
ParallelThreshold
OptimizingPartitioning
Single Complete Average
Clustering Procedures
NonhierarchicalHierarchical
Agglomerative Divisive
Ward’s Method
LinkageMethods
VarianceMethods
CentroidMethods
Fig. 20.4
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Hierarchical clustering is characterized by the development of a hierarchy or tree-like structure. Hierarchical methods can be agglomerative or divisive. Agglomerative clustering starts with each object in a separate cluster. Clusters are formed by grouping objects into bigger and bigger clusters. This process is continued until all objects are members of a single cluster. Divisive clustering starts with all the objects grouped in a single cluster. Clusters are divided or split until each object is in a separate cluster. Agglomerative methods are commonly used in marketing research. They consist of linkage methods, error sums of squares or variance methods, and centroid methods.
Conducting Cluster Analysis Select a Clustering Procedure – Hierarchical
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The single linkage method is based on minimum distance, or the nearest neighbor rule. At every stage, the distance between two clusters is the distance between their two closest points (see Figure 20.5). The complete linkage method is similar to single linkage, except that it is based on the maximum distance or the furthest neighbor approach. In complete linkage, the distance between two clusters is calculated as the distance between their two furthest points. The average linkage method works similarly. However, in this method, the distance between two clusters is defined as the average of the distances between all pairs of objects, where one member of the pair is from each of the clusters (Figure 20.5).
Conducting Cluster Analysis Select a Clustering Procedure – Linkage Method
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Linkage Methods of ClusteringSingle Linkage
Minimum Distance
Complete Linkage
Maximum Distance
Average Linkage
Average Distance
Cluster 1 Cluster 2
Cluster 1 Cluster 2
Cluster 1 Cluster 2
Fig. 20.5
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Other Agglomerative Clustering Methods
Ward’s Procedure
Centroid Method
Fig. 20.6
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SPSS Windows
To select this procedures using SPSS for Windows click:
Analyze>Classify>Hierarchical Cluster …
Analyze>Classify>K-Means Cluster …