Measuring Multidimensional Concepts: Indexes and Scales

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Measuring Multidimensional Concepts Indexes and
Scales
Andrew Austin ? 2009
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Introduction
Multidimensional conceptsVariables that have no
obvious single indicator, e.g., attitudes,
beliefs. Multiple observations of a
conceptseveral items that provide indications of
a theoretical constructs, i.e., a
variable. Composite measurescombining several
measures into a single measure. Two
types Indices (or indexes)Indices are
constructed by adding together the scores of
multiple indicators of the same concept (e.g.
counting the number of sexist statements.) Scales
A scale assigns values based on patterns of
responses. They assume that some indicators
indicate more of the concept than others.
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Why do we use indices and scales?
Increasing range and variationsome variables do
not have the desired range and variation. Greater
efficiency in data analysisindices and scales
offer comprehensive and accurate measures.
Rather than a large sample using a rough
indicator of a construct, greater precision may
be achieved with smaller samples. Increasing
validity and reliabilitymore shots at a target
make a bulls eye more likely.
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Indices
Indices are constructed by adding together the
scores of multiple indicators of the same concept.
Example Race Prejudice Index Code each response
0 disagree, 1 agree Combine responses range
0 4 Score index 0 no race prejudice, 4
most race prejudice
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Example (continued)
Indicate whether you agree or disagree with each
of the following statements by circling the
letter that best represents your views
1.      On the whole, blacks are lazier than
whites. a.      Agree b.      Disagree 2.     
For the most part, blacks are responsible for
their problems in America. a.      Agree b.     
Disagree 3.      On average, blacks tend to be
more violent than whites. a.      Agree b.     
Disagree 4.      Blacks are generally more
sexual promiscuous (engage in sexual relations)
than whites. a.      Agree b.      Disagree
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Evaluating Index Prior to Data Collection
Consider the face, content, and construct
validity. Consider the possible range and
variability of the indexDo the indicators
measure several dimensions of the same
concept? Consider whether any of the indicators
might be unreliableEach must tap the theoretical
construct approximately equally.
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Evaluating Index after Data have been Collected
Check for criterion-related validity. Factor
analysiscorrelations between two or more
variables become indicators of a latent variable
or factor. Principal component analysis and
principal factor analysis detect patterns among
correlations. Checking reliability using
Cronbach's alphathis is a test of an indexs
internal consistency. Internal consistencythe
extent to which scores on items correlate with
each other.
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Examples of Factors
Activities of daily living combines ability to
feed oneself, clothes oneself, and groom
oneself. General intelligence factor combines
analytical ability, verbal ability,
spatial-relational ability, mathematical
ability. Curiosity combines interest in reading,
interest in science, interests in puzzles.
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Scales
A scale assigns values based on patterns of
responses. They assume that some indicators
indicate more of the concept than others. Types
of scales Bogardus Social distance scale Thurston
Scales Likert scales Gutman Scales Semantic
Differential Scale
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Likert scale example
Likert scale items assessing sexist attitudes
toward women (adapted from the Neosexism Scale
Tougas, Brown, Beaton, Joly, 1995) (Items with
an asterisk are reverse-scored.) Discrimination
against women in the labor force is no longer a
problem in the United States. totally disagree
1 2 3 4 5 6 7 totally agree I consider the
present employment system to be unfair to
women. totally disagree 1 2 3 4 5 6 7
totally agree It is difficult to work for a
female boss. totally disagree 1 2 3 4 5 6
7 totally agree In order not to appear sexist,
many men are inclined to overcompensate
women. totally disagree 1 2 3 4 5 6 7
totally agree In a fair employment system, men
and women would be considered equal. totally
disagree 1 2 3 4 5 6 7 totally agree
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Semantic differential scale assessing attitudes
toward African Americans Blacks are dirty
___________________________________
clean (-3) (-2) (-1)
( 0) (1) (2) (3) friendly
___________________________________
unfriendly (-3) (-2)
(-1) ( 0) (1) (2) (3)
bad ___________________________________
good (-3) (-2) (-1)
( 0) (1) (2) (3) beautiful
___________________________________ ugly
(-3) (-2) (-1) ( 0)
(1) (2) (3)
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Thurstone scale example
Thurstone scale items assessing attitudes toward
euthanasia (Tordella Neutens, 1979) Each items
scale values (range 1 to 5) is given in
parentheses. Respondents do not know the
values. A person with a terminal illness has the
right to decide to die. (4.15) Inducing death for
merciful reasons is wrong. (1.65) A person should
not be kept alive by machines. (2.44) Euthanasia
gives a person a chance to die with dignity.
(4.29) The taking of human life is wrong no
matter what the circumstances. (1.36)