Comparative ScalingComparative Scaling

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

• 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

Primary Scales

Nominal Scale

Ordinal Scale

RatioScale

IntervalScale

Primary Scales of Measurement

• Nominal– A scale in which the numbers or letters

assigned to objects serve as labels for identification or classification.

• Ordinal– A scale that arranges objects or

alternatives according to their magnitude in an ordered relationship.

Primary Scales of Measurement

• Interval– A scale that both arranges objects

according to their magnitudes and

– Distinguishes the ordered arrangement in units of equal intervals

– I.e., indicate order and measure order (or distance) in units of equal intervals

Primary Scales of Measurement

• Ratio–A scale that has absolute rather than

relative quantities and an absolute zero where a given attribute is absent.

–Money & weight are good examples of attributes that possess absolute zeros and interval properties.

Primary Scales of Measurement

Scale

Nominal Numbers Assigned 16 24 17 to Drivers/Cars

Ordinal Rank Order Third Second First of race finishers Place Place Place

Interval Championship Points earned 170 175 185

Ratio Time to Finish, behind winner 5.1 2.3 0.0

Primary Scales of Measurement

• Comparative Scales–Involve the direct comparison of

two or more objects

• Noncomparative Scales–Objects or stimuli are scaled

independently of each other.

Classifying Scaling Techniques

ScalingTechniques

ComparativeScales

PairedComparison

ConstantSum

RankOrder

NoncomparativeScales

ItemizedRating Scales

Continuous Rating Scales

Likert

Semantic Differential

Stapel

Classifying Scaling Techniques

• 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.

Non-Comparative ScalingNon-Comparative Scaling

Noncomparative Rating Scales

ContinuousRating Scales

ItemizedRating Scales

SemanticDifferential

Stapel Likert

Classifying Noncomparative Scaling Techniques

Continuous Rating Scale Example

VeryPoor

VeryGood

0 10 20 30 40 50 60 70 80 90 100

X

Method of Summated Ratings: The Likert Scale

• Extremely popular means for measuring attitudes.

• Respondents indicate their own attitudes by checking how strongly they agree/disagree with statements.

• Response alternatives: – “strongly agree”, “agree”, “uncertain”,

“disagree”, and “strongly disagree”.

• Generally use either a 5- or 7-point scale

Semantic Differential Scales

• A series of numbered (usually seven-point) bipolar rating scales.

• Bipolar adjectives (for example, “good” and “bad”), anchor both ends (or poles) of the scale.

• A weight is assigned to each position on the rating scale. – Traditionally, scores are 7, 6, 5, 4, 3, 2, 1, or

+3, +2, +1, 0, -1, -2, -3.

Semantic Differential Scales for Measuring Attitudes Toward Tennis

Exciting ___ : ___ : ___ : ___ : ___ : ___ : ___ : Calm

Interesting ___ : ___ : ___ : ___ : ___ : ___ : ___ : Dull

Simple___ : ___ : ___ : ___ : ___ : ___ : ___ Complex

Passive ___ : ___ : ___ : ___ : ___ : ___ : ___ Active

Stapel Scales

• Modern versions of the Stapel scale place a single adjective as a substitute for the semantic differential when it is difficult to create pairs of bipolar adjectives.

• The advantage and disadvantages of a Stapel scale, as well as the results, are very similar to those for a semantic differential.

• However, the Stapel scale tends to be easier to conduct and administer.

A Stapel Scale for Measuring a Store’s Image

Department

Store Name

+3

+2

+1

Wide Selection

-1

-2

-3

Graphic Rating Scales

A graphic rating scale presents respondents with a graphic continuum.

Graphic Rating Scale Stressing Pictorial Visual Communications

3 2 1Very VeryGood Poor

Surfing the Internet is

____ Extremely Good

____ Very Good

____ Good

____ Bad

____ Very Bad

____ Extremely Bad

Surfing the Internet is

____ Extremely Good

____ Very Good

____ Good

____ Somewhat Good

____ Bad

____ Very Bad

Balanced Scale Unbalanced Scale

Balanced and Unbalanced Scales

Summary of Itemized Rating Scale Decisions

1. Number of categories While there is no single, optimal number, traditional guidelines

suggest that there should be between five and nine categories.

2. Balanced vs. unbalanced In general, the scale should be balanced to obtain objective data.

3. Odd or even number of If a neutral or indifferent scale response is possible for

categories at least some of the respondents, an odd number of categories

should be used.

Summary of Itemized Rating Scale Decisions (continued)

4. Forced versus nonforced In situations where the respondents are expected

to have no opinion, the accuracy of data may be

improved by a nonforced scale.

5. 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.

6. Physical form A number of options should be tried and the best

one selected.

Scale Evaluation

Scale Evaluation

Reliability Validity

Test-RetestInternal

ConsistencyAlternative Forms Construct

Criterion

Content

Convergent Validity

Discriminant Validity Nomological

Validity

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)