Measurement, Scaling and Attitude Scales

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Chapter 9 10

• Measurement, Scaling and Attitude Scales

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Topics

• Concept of measurement and scaling
• Types scales primary scales
• Approaches to scaling
• comparative scaling techniques
• noncomparative techniques
• Validity and reliability

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Measurement and Scaling definitions

• Measurement
• Process of assigning numbers or labels to things
  to represent quantities or qualities of
  attributes according to some rule.
• Rule
• A guide for making the assignment.
• Scaling
• Identification of the symbols or numbers to be
  assigned by a rule to the individuals (or their
  behaviors or attitudes) to whom the scale is
  applied.

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Measurement and Scaling definitions (revised)

• Measurement
• the process of assigning categories (e.g.,
  numbers) to concepts using some rule
• Rule
• the method of assignment
• Scaling
• the creation of the categories (e.g., the
  underlying continuum) used in measurement
• Scale the continuum

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Concepts and Constructs

• Concept
• an abstract idea
• e.g., day, month, year
• Construct
• a higher level abstraction of an ideahigher
  level concepts
• e.g., time

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Types of Measurement Scales (1)

• Nominal Scales
• Scales that partition data into mutually
  exclusive and collectively exhaustive categories.
• Ordinal Scales
• Nominal scales that reflect order.

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Types of Measurement Scales (2)

• Interval Scales
• Ordinal scales with equal intervals between
  points
• may include an arbitrary zero point.
• Ratio Scales
• Interval scales with a meaningful zero point so
  that magnitudes can be compared arithmetically.

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What Type of Scale?
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Can usually categorize scale as

• Discrete (categorical)
• nominal (classification) or
• ordinal
• Metric (continuous)--amount of something
• interval
• ratio

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Types of Scale Representations

• Graphic Rating Scales
• Graphic continua anchored by two extremes
• Itemized Rating Scales
• Scales in which the respondent selects an answer
  from a limited number of ordered categories.

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Types of Attitude Scales (1)

• Comparative Scales
• require comparison of one object, concept, or
  person against another.
• Rank-Order Scales
• requires comparing one item with another or a
  group of items against each other and ranking
  them.
• Pared Comparison
• require picking one of two objects in a set based
  on some stated criteria.

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Types of Attitude Scales (2)

• Comparative scales (continued)
• Q-Sorting
• form or rank-ordering using card sorts and
  assumed distributions .
• Constant Sum Scales
• Attributes based on their relative importance to
  the person

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Constant sum scale
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Types of Attitude Scales (3)

• Non-comparative scales
• scales requiring independent judgments
• Likert Scale
• requires specifying a level of agreement or
  disagreement with statements about a referent
• Semantic Differential Scale
• require rating in terms of a series of bipolar
  adjectives

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Likert scale
Cal Poly is a great university for business majors
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T101 RIP 9.2 A Semantic Differential Scale for
Measuring Self Concepts, Person Concepts, and
Product Concepts
1. Rugged----------------------
------Delicate 2. Excitable--------
--------------------Calm 3.
Uncomfortable----------------------------C
omfortable 4. Dominating---------------
-------------Submissive 5.
Thrifty----------------------------Indulge
nt 6. Pleasant-------------------
---------Unpleasant 7. Contemporary--------
--------------------Noncontemporary 8.
Organized----------------------------U
norganized 9. Rational------------
----------------Emotional 10.
Youthful----------------------------Mature
11. Formal--------------------
--------Informal 12.
Orthodox----------------------------Libera
l 13. Complex---------------------
-------Simple 14. Colorless---------
-------------------Colorful 15.
Modest----------------------------Vain
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Types of Attitude Scales (4)

• Non-comparative scales (continued)
• Stapel scale
• An adaptation of semantic differential--requires
  rating how close and in what direction an
  adjective fits a concept

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Stapel Scale
5 4 3 2 1 Friendly -1 -2 -3 -4 -5
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True Score Model

• Xo Xt Xs Xr
• Xo Observed Score
• Xt True Score
• Xs Systematic Error
• Xr Random Error

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Types of Measurement Error

• Systematic Error
• Error that results in a constant bias in the
  measurements.
• Random Error
• Error that affects measurement in a transient,
  inconsistent manner.

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Sources of Measurement Differences

• Accurate data implies accurate measurement, or M
  A, where M refers to measurement and A stands
  for complete accuracy.
• Rarely found in market research
• Typically
• M A E
• where E errors

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Reliability Validity

• Reliability
• Degree to which measures are free from random
  error and, therefore, provide consistent data
• Validity
• Extent to which a measurement instrument actually
  measures the attribute it was intended to measure

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Reliability Measures

• Test-retest give same test at different times to
  same people
• Alternative forms develop different but
  equivalent forms--administer at different times
• Internal consistency
• split-half physically divide
• Coefficient alpha average of all possible
  split-half reliability coefficients

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Reliability Analysis (3)
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College Drinking DataParty Animal scale
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Reliability Analysis (2)
R E L I A B I L I T Y A N A L Y S I S - S
C A L E (A L P H A) Item-total Statistics
Scale Scale Corrected
Mean Variance Item-
Alpha if Item if
Item Total if Item
Deleted Deleted Correlation
Deleted ANIMAL 12.8333 24.5396
.5444 .6411 PARENTS 12.6882
26.8320 .2106 .7055 YOURSELF
12.7581 24.9952 .6169
.6402 NIGHTS 13.4194 23.0448
.6440 .6116 HOWMANY 10.4892
10.9864 .5806 .7276 REMEMBER
12.9194 22.8637 .5735
.6197 Reliability Coefficients N of Cases
186.0 N of Items 6 Alpha
.6924
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Reliability Analysis (3)
R E L I A B I L I T Y A N A L Y S I S - S
C A L E (A L P H A) Item-total Statistics
Scale Scale Corrected
Mean Variance Item-
Alpha if Item if Item
Total if Item
Deleted Deleted Correlation
Deleted ANIMAL 8.3011 7.8224
.4768 .6856 PARENTS 8.1559
8.8242 .1812 .7991 YOURSELF
8.2258 7.7325 .6540
.6367 NIGHTS 8.8871 6.6737
.6537 .6110 REMEMBER 8.3871
6.4980 .5818
.6408 Reliability Coefficients N of Cases
186.0 N of Items 5 Alpha
.7276
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Reliability Analysis (3)
R E L I A B I L I T Y A N A L Y S I S - S
C A L E (A L P H A) Item-total Statistics
Scale Scale Corrected
Mean Variance Item-
Alpha if Item if
Item Total if Item
Deleted Deleted Correlation
Deleted ANIMAL 5.9677 5.6963
.5502 .7773 YOURSELF 5.8925
5.8262 .6821 .7318 NIGHTS
6.5538 4.9620 .6558
.7262 REMEMBER 6.0538 4.6998
.6081 .7598 Reliability
Coefficients N of Cases 186.0
N of Items 4 Alpha .7991
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Validity

• degree too which the observed score measures
  true score--i.e., true difference between objects
  for characteristic being measured
• therefore, reflects absence of total error (Xs
  and Xr)
• essential to generalizability

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Types of Validity

• Content (face) validity does measure appear to
  measure what is intended
• Criterion validity does measure behave as
  expected in relation to other measures
• Convergent Validity
• Divergent Validity

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Illustrations of Possible Reliability and
Validity Relationship
Situation 1
Situation 3
Situation 2
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Neither reliable nor Valid
Highly reliable but not valid
Highly reliable and valid
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