Measurement and Scaling

By Rama Krishna Kompella

Learning Objectives

• Understand the role of measurement in marketing research

• Explain the four basic levels of scales• Describe scale development and its

importance gathering primary data• Discuss comparative and

noncomparative scales

Basic Measurement IssuesMeasurement is the process of assigning numbers or

labels to objects, persons, states, or events in accordance with specific rules to represent quantities or qualities of attributes.

We do not measure specific objects, persons, etc., we measure attributes or features that define them.

Ex., What defines the person Brent Wren? What is a student’s level of education? How customer oriented is our company?

Overriding Goal: To provide a valid and reliable description or enumeration of the person, objects, issue, etc.

Accuracy of Measurements Why do scores on a measurement scale differ?◦ A true difference in the characteristic being

measured.◦ Short-term personal factors (e.g., moods, time

constraints)◦ Situational factors (e.g., surroundings)◦ Variations in method of administering survey.◦ Sampling of items included in the questionnaire.◦ Lack of clarity in the measurement instrument.◦ Mechanical or instrument factors causing

completion errors.

Measurement Process

1. Define concepts to be measured2. Define attributes of the concepts3. Select scale of measurement (data type)4. Generate Items/Questions

– Wording– Response format

5. Layout and design questionnaire6. Pretest and refine

Some Key Concepts• Measurement

– Assigning numbers or other symbols to characteristics of objects being measured, according to predetermined rules.

• Concept (or Construct)– A generalized idea about a class of objects, attributes,

occurrences, or processes.• Relatively concrete constructs

– Age, gender, number of children, education, income• Relatively abstract constructs

– Brand loyalty, personality, channel power, satisfaction

• Scaling– The generation of a continuum upon which measured

objects are located.• Scale

– A quantifying measure – a combination of items that is progressively arranged according to value or magnitude.

– Purpose is to quantitatively represent an item’s, person’s, or event’s place in the scaling continuum.

Some Key Concepts

Nominal ScalesNominal Scales

Ordinal ScalesOrdinal Scales

Interval ScalesInterval Scales

Ratio ScalesRatio Scales

Four Basic Scales of Measurement

Bob

Gene

Sam

Primary Scales of MeasurementScaleNominal Symbols

Assigned to Runners

Ordinal Rank Orderof Winners

Interval PerformanceRating on a

0 to 10 Scale

Ratio Time to Finish, in

Seconds

3rd place 2nd place 1st place

Finish

Finish

3 7 9

15.2 14.1 13.4

Primary Scales of MeasurementNominal Scale

• The numbers serve only as labels or tags for identifying and classifying objects.

• When used for identification, there is a strict one-to-one correspondence between the numbers and the objects.

• The numbers do not reflect the amount of the characteristic possessed by the objects.

• The only permissible operation on the numbers in a nominal scale is counting.

• Only a limited number of statistics, all of which are based on frequency counts, are permissible, e.g., percentages, and mode.

Primary Scales of MeasurementOrdinal Scale

• A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic.

• Can determine whether an object has more or less of a characteristic than some other object, but not how much more or less.

• Any series of numbers can be assigned that preserves the ordered relationships between the objects.

• In addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on centiles, e.g., percentile, quartile, median.

Primary Scales of MeasurementInterval Scale

• Numerically equal distances on the scale represent equal values in the characteristic being measured.

• It permits comparison of the differences between objects. For example, the difference between 1 and 2 is the same as between 3 and 4. The difference between 1 and 9 (i.e., 8) is twice as large as the difference between 2 and 4 (i.e., 2) or 6 and 8 (2).

• The location of the zero point is not fixed. Both the zero point and the units of measurem. are arbitrary.

• It is NOT meaningful to take ratios of scale values• It IS meaningful to take ratios of their differences. • Statistical techniques that may be used include all of those that can be

applied to nominal and ordinal data, and in addition the arithmetic mean, standard deviation, correlation, and other common statistics.

• But NOT: geometric or harmonic mean, nor CV = S/X

Primary Scales of MeasurementRatio Scale

• Possesses all the properties of the nominal, ordinal, and interval scales.

• It has an absolute zero point. Examples: height, weight, age, money, sales, costs, market share, number of customers, the rate of return.

• It is meaningful to compute ratios of scale values. • For example, not only is the difference between 2 and 5 the

same as the difference between 14 and 17, but also 14 is seven times as large as 2 in an absolute sense.

• All statistical techniques can be applied to ratio data.

Primary Scales of Measurement

Scale Basic Characteristics

Common Examples

Marketing Examples

Nominal Numbers identify & classify objects

Social Security nos., numbering of football players

Brand nos., store types

Percentages, mode

Chi-square, binomial test

Ordinal Nos. indicate the relative positions of 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

Ratio Zero point is fixed, ratios of scale values can be compared

Length, weight Age, sales, income, costs

Geometric mean, harmonic mean

Coefficient of variation

Permissible Statistics Descriptive Inferential

Interval Differences between objects

Temperature (Fahrenheit)

Attitudes, opinions, index

Range, mean, standard

Product-moment

Generate Items• Items are basically questions• Need to ensure that enough questions are

asked to generate information necessary to address research problems.

• Likely will have a mix of question types and scales of measurement

• Multi-item, Composite or Index Measures– A measurement scale containing multiple questions

addressing same construct or attribute

A Classification of Scaling Techniques

Likert Semantic Differential

Stapel

Scaling Techniques

NoncomparativeScales

Comparative Scales

Constant Sum

Paired Comparison

Rank Order

Q-Sort and

Other Procedures

Continuous Rating Scales

Itemized Rating Scales

• Respondent is presented with two objects at a time

• Then asked to select one object in the pair according to some criterion

• Data obtained are ordinal in nature– Arranged or ranked in order of magnitude

• Easy to do if only a few items are compared.• If number of comparisons is too large,

respondents may become fatigued and no longer carefully discriminate among them.

Paired Comparison Scaling

Paired Comparison Scaling: Example

Cunningham Day Parker Thomas

Cunningham 0 0 0

Day 1 1 0

Parker 1 0 0

Thomas 1 1 1 0

# of times preferred 3 1 2 0

For each pair of professors, please indicate the professor from whom you prefer to take classes with a 1.

• Respondents are presented with several objects simultaneously

• Then asked to order or rank them according to some criterion.

• Data obtained are ordinal in nature– Arranged or ranked in order of magnitude

• Commonly used to measure preferences among brands and brand attributes

Rank Order Scaling

Rank Order Scaling

Instructor Ranking

Cunningham 1

Day 3

Parker 2

Thomas 4

Please rank the instructors listed below in order of preference. For the instructor you prefer the most, assign a “1”, assign a “2” to the instructor you prefer the 2nd most, assign a “3” to the instructor that you prefer 3rd most, and assign a “4” to the instructor that you prefer the least.

• Respondents are asked to allocate a constant sum of units among a set of stimulus objects with respect to some criterion

• Units allocated represent the importance attached to the objects.

• Data obtained are interval in nature• Allows for fine discrimination among

alternatives

Constant Sum Scaling

Constant Sum Scaling

Instructor Availability Fairness Easy Tests

Cunningham 30 35 25

Day 30 25 25

Parker 25 25 25

Thomas 15 15 25

Sum Total 100 100 100

Listed below are 4 marketing professors, as well as 3 aspects that students typically find important. For each aspect, please assign a number that reflects how well you believe each instructor performs on the aspect. Higher numbers represent higher scores. The total of all the instructors’ scores on an aspect should equal 100.

Graphic Rating Scale

A Classification of Scaling Techniques

Likert Semantic Differential

Stapel

Scaling Techniques

NoncomparativeScales

Comparative Scales

Paired Comparison

Rank Order

Constant Sum

Q-Sort and Other Procedures

Continuous Rating Scales

Itemized Rating Scales

Continuous Rating Scale Example

VeryPoor

VeryGood

0 10 20 30 40 50 60 70 80 90 100

X

Likert ScaleA likert scale is an ordinal scale format that asks respondents to indicate the extent to which they agree or disagree with a series of mental or behavioral belief statements about a given object

Likert Scale Example

Semantic Differential Scale

A semantic differential scale is unique bipolar ordinal scale format that captures a person’s attitudes and/or feelings about a given object

Semantic Differential Scale Format

Behavioral Intention Scale

A behavioral intention scale is a special type of rating scale designed to capture the likelihood that people will demonstrate some type of predictable behavior intent toward purchasing an object or service in a future time frame

Shopping Intention Scale

Scale EvaluationScale

Evaluation

ReliabilityValidity

Test-RetestInternal

ConsistencyAlternative

Forms Construct

Criterion

Content

Convergent Validity

Discriminant Validity

NomologicalValidity

Reliability• Extent to which a scale produces consistent

results• Test-retest Reliability

– Respondents are administered scales at 2 different times under nearly equivalent conditions

• Alternative-form Reliability– 2 equivalent forms of a scale are constructed, then

tested with the same respondents at 2 different times

Reliability• Internal Consistency Reliability

– The consistency with which each item represents the construct of interest

– Used to assess the reliability of a summated scale– Split-half Reliability

• Items constituting the scale divided into 2 halves, and resulting half scores are correlated

– Coefficient alpha (most common test of reliability)• Average of all possible split-half coefficients resulting from

different splittings of the scale items

Validity• Extent to which true differences among the objects are

reflected on the characteristic being measured• Content Validity

– A.k.a., face validity– Subjective, but systematic evaluation of the

representativeness of the content of a scale for the measuring task at hand

• Criterion Validity– Examines whether measurement scale performs as expected

in relation to other variables selected as meaningful criteria– I.e., predicted and actual behavior should be similar

Construct Validity• Addresses the question of what construct or

characteristic the scale is actually measuring• Convergent Validity

– Extent to which scale correlates positively with other measures of the same construct

• Discriminant Validity– Extent to which a measure does not correlate with other

constructs from which it is supposed to differ• Nomological Validity

– Extent to which scale correlates in theoretically predicted ways with measures of different but related constructs

Relationship Between Reliability and Validity

• A scale can be reliable, but not valid• In order for a scale to valid, it must also be reliable.• In other words,

– Reliability is a necessary but insufficient condition for Validity.

Reliability and Validity on Target

Old Rifle New Rifle New Rifle SunglareLow Reliability High Reliability Reliable but Not

Valid(Target A) (Target B) (Target C)

Q & As