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Measurement and Scaling

• Terms to know

• Discussion questions and topics (4)

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Measurement and Scaling

• Operational Definitions• Measuring Constructs• Types of Scales • Discussion Questions and Topics (4)• Development of Scales

– Example: Consumer Discontent Scale

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Operational Definition

• Stating a construct in terms of its dimensions and elements so that it becomes measurable.

• Examples:

Learning

Stress

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MEASUREMENT

• Assignment of numbers to the characteristics of objects, people,states, or events according to rules.

– Numbers

– Characteristics of objects, etc.

– Rules

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Assessing a Respondent’s Liking of Soft DrinksWith Nominal, Ordinal, Interval, and Ratio Scales

NominalWhich of the soft drinks in the following list do you like? (Check ALL that apply):

___Coke___Dr. Pepper___Mountain Dew___Pepsi___Seven Up___Sprite

OrdinalRank the soft drinks according to how much you like each (most preferred drink = 1, and least preferred drink = 6):

___Coke___Dr. Pepper___Mountain Dew___Pepsi___Seven Up___Sprite

IntervalPlease indicate how much you like each soft drink by checking the appropriate position on thescale: dislike like

a lot dislike like a lotCoke ____ ____ ____ ___Dr. Pepper ____ ____ ____ ___Mountain Dew ____ ____ ____ ___Pepsi ____ ____ ____ ___Seven Up ____ ____ ____ ___Sprite ____ ____ ____ ___

RatioPlease divide 100 points among these soft drinksTo represent how much you like each:

___Coke___Dr. Pepper___Mountain Dew___Pepsi___Seven Up___Sprite100

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• The brands to be rated are presented two at a time, so

each brand in the category is compared once to every

other brand

• Compare Nestle with Milka

Nestle with Eti

Milka with Eti

Paired Comparison Scale (ordinal)

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Likert Summated Rating Form (interval)

neitherstrongly agree nor stronglydisagree disagree disagree agree agree

1. The bank offers courteous service. ___ ___ ___ ___ ___

2. The bank has a convenient location. ___ ___ ___ ___ ___

3. The bank has convenient hours. ___ ___ ___ ___ ___

4. The bank offers low interest rate loans. ___ ___ ___ ___ ___

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Semantic Differential Scaling Form (interval)

Service is discourteous ___:___:___:___:___:___:___ Service is courteousLocation is convenient ___:___:___:___:___:___:___ Location is inconvenientHours are convenient ___:___:___:___:___:___:___ Hours are inconvenientLoan interest rates are high ___:___:___:___:___:___:___ Loan interest rates are low

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Contrasting Profiles of Banks A and B (derived from semantic differential scale)

Service is discourteous ___:___:___:___:___:___:___ Service is courteous

Location is convenient ___:___:___:___:___:___:___ Location is inconvenient

Hours are convenient ___:___:___:___:___:___:___ Hours are inconvenient

Loan interest rates are high ___:___:___:___:___:___:___ Loan interest rates are low

Bank ABank B

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Comparative Judgement Scale (interval)

• Compared to Signal, Colgate’s whitening power is:– Much better– Better– About the same– Worse– Much worse

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Graphic Rating Scale (ratio)

Please evaluate each quality in terms of how important it isto you personally by clicking the cursor at the position on thehorizontal line that most reflects your feelings:

not veryimportant

importantCourteous service

_______________________________________

Convenient location _______________________________________

Convenient hours_______________________________________

Low interest rate loans _______________________________________

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Constant Sum Scale (ratio)

Please divide 100 points among the following bank services in terms of relatively how important each is to you:

___Courteous service___Convenient hours___Convenient location___Low interest rates100

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Sad-to-Happy Faces that Work with Children (and Adults!)

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Discussion Questions and Topics (4)

Measurement and Scaling

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Terms to know

• Operational definition • Measurement of constructs• Scaling types as tools:

– Nominal– Ordinal– Interval– Ratio

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What are the sources of variation in measured score?

• True differences• Stability in individual characteristics• Transient factors• Situational Factors• Variations in administration• Sampling of items• Clarity of measurement instrument• Mechanical factors

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Comment and Prove

• If a measure is valid, then it is reliable.

• XO=XT+XS+XR– XO= Observed Score– XT= True Score– XS= Systematic Error– XS= Random Erro

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How doyou infer validity of a measure?

• Indirect Evidence by reliability– Where XR=0

• Direct evidence by validity– Where XO=XT

• Domain Sampling Model

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Indirect EvidenceVia ReliabilityCoefficients

Direct EvidenceVia ValidityCoefficients

Test-retest

Alternate forms

Split half

Coefficient

Predictive validity

Content validity

Construct validity

Convergent validity

Discriminant validity

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What is the procedure for scale development?

• Let’s look at Consumer Discontent Scale and identify the steps in developing this scale?

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The Development of a Scale to Measure Consumer Discontent

William J. Lundstrom

Lawrence M. Lamont

Journal of Marketing Research, Nov. 1976

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Procedure for Scale Development

1. Definition of the construct and development of scale statements

2. Selection of the type of scaling procedure

3. Selection of items for testing of scale properties

4. Reliability testing of scale properties

5. Validation of final scale properties

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Step1: Definition of the Construct and Development of Scale Statements

• Comprehensive literature review

• Scope of consumer discontent

– The product strategies of business

– Business communications and information

– Impersonal nature of business & retail institutions

– Socioeconomic and political forces

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Definition of the Construct and Development of Scale Statements

Initial Item Pool

Edited ItemPool

PreliminaryForm of the

Scale

173 Statements 118 Statements 99 Statements

10 Judges

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Scaling Procedure

• Likert-type scales (Summated Ratings)

– Six-point interval scaled from “strongly agree” to “strongly disagree”

– Total attitude score for each respondent

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Item Analysis and Selection

• Assessing an item’s ability to differentiate significantly between subjects

• 99 statements, 309 respondents

• t-test– Respondents’ summated item scores (highest to lowest)

– Highest 25% and lowest 25% used as criterion groups

– Determining statements showing a statistically significant difference

– 84 items retained for reliability testing

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Validity Testing• Construct Validity

– Internal validity analysis• Scale homogeneity and consistency• Correlation of each statement with the total score• Final version of the scale - 82 items

– External validity analysis• Whether scale score could distinguish between 'known

groups’ of persons holding different attitudes• Sample: Contended group (100) & discontended group

(180)• z-test - significant difference between two groups

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Reliability Testing

• Test Reliability (226 subjects)

– Split-half – internal consistency• Split-half reliability coefficient (uncorrected) - .96

(Flanagan formula)

• Split-half reliability coefficient (corrected) - .94

(Spearman-Brown prophecy formula)

– Test-retest – temporal accuracy• Test-retest reliability coefficient - .79

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• Response Bias Reliability (226 subjects)

– Agreement response scale (Couch & Kenniston)

– Social desirability scale (Crowne & Marlowe)

– Consumer discontent measure is not affected by respondent tendencies to answer in an acquiescent or socially desirable manner

Reliability Testing

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Consumer Discontent Scale

• Scale name and composition– Name: only one pole of bipolar construct– Composition: Negative response bias

• Use of the scale– Self report scale– Respondent’s total score = sum (or mean) of

the scores across statements

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