Indexes, Scales, and Typologies

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Chapter 6

• Indexes, Scales, and Typologies

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Two familiar indexes

• Consumer Price Index
• Dow Jones Industrial Average

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What happens when complex concepts cannot be
measured with single variables?

• Example Religiosity
• Religion - a set of cultural ideas, symbols, and
  practices that focus on the meaning of life and
  the nature of the unknown
• Religiosity - the extent to which a person
  believes in and practices a religion

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Some aspects of religiosity

• Attending religious services
• Personal participation in religious rituals when
  not at services (e.g., prayer)
• Assisting or leading meetings of religious
  organizations
• Having religious visions or experiences
• Believing in religious dogma
• Giving material support to religious organizations

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Survey measurement of religiosity

• Measure each aspect of religiosity with a
  separate question.
• Analysis options
• Analyze each question separately
• Develop an index or scale as a single measure
  which summarizes the results of two or more
  separate questions.

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What is an index?

• A composite measure, combining responses to two
  or more separate variables
• A survey respondents score on an index is
  determined by the responses given to two or more
  separate questions, each of which measures an
  aspect of the concept.
• An index is constructed through the simple
  summation of numerical scores received on each
  component question.

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Index Construction

• 1. Item selection
• 2. Index scoring
• 3. Examination of empirical relationships
• 4. Handling missing data

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1. Item selection Criteria

• (1) Face validity
• (2) Unidimensionality
• (3) Variance

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Item selection criteria (1) Face/logical
validity

• Each item on the face of it should appear to
  measure the concept
• Examples
• Dont include an item measuring level of fear of
  walking outside at night in your index of
  religiosity.
• Dont include an item measuring attitude toward
  abortion in your index of religiosity.

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Item selection criteria (2) Unidimensionality

• Babbie (p. 150) the index should represent
  only one dimension of a concept (e.g., one index
  for religious participation another index for
  religious beliefs).
• From Ch. 5 Dimensions - different facets or
  aspects of the concept
• However, Babbies next point (General or
  Specific) indicates that something more general
  than a single dimension could be measured e.g.,
  religiosity as a combination of different types
  of religiosity (so, one index combining religious
  participation and belief).

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• This is confusing. In index construction, many
  researchers use the term unidimensionality to
  mean that all the items should measure a single
  concept.
• (Note, however, that this meaning differs from
  the use of dimension in the conceptualization
  process.)
• Therefore, I use the term here to mean that all
  items in my index must measure religiosity and
  not some other concept, such as alienation,
  anomie, or political ideology.

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Item selection criteria (3) Variance

• The resulting index should rank respondents from
  low to high with regard to the concept.
• (NOTE You will not know this until you actually
  construct the index and run a frequency
  distribution on it.)
• The index should show decent variance e.g., not
  classify almost everyone as high on religiosity.
• (NOTE Or this!)
• Thus, as a group, the items must rank some
  respondents as low on religiosity and some as
  high.

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Sample item selections for Religiosity Index from
GSS 2000

• How often do you attend religious services?
  (ATTEND)
• I am going to name some institutions in this
  country. As far as the people running these
  institutions are concerned, would you say you
  have a great deal of confidence, only some
  confidence, or hardly any confidence at all in
  them? Organized religion (CONCLERG)
• Which of these statements comes closest to
  describing your feelings about the Bible? (BIBLE)
• About how often do you pray? (PRAY)
• How good would you say your local church worship
  services are? (WORSHIP)

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Index Construction

• 1. Item selection
• 2. Index scoring
• 3. Examination of empirical relationships
• 4. Handling missing data

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2. Index scoring

• Determine how each item should be scored
• All items need to be scored in the same
  direction. A high value on one item must mean
  the same thing with regard to the concept as a
  high value on all others.
• If not, the coding of the offending item(s) needs
  to be reversed, using SPSS recode feature
• Consider
• Range of measurement vs. adequate number of cases
  at each point in resulting index
• Equal item weights or differing item weights

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Item scoring - ATTEND
Low Religiosity (0)
High Religiosity (1)
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Item scoring - CONCLERG
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Item scoring - BIBLE
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Item scoring - PRAY
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Item scoring - WORSHIP
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Open SPSS and relindex.sav (in the class data
files directory)

• The variables have been recoded
• ATTEND ATTENDR
• CONCLERG CLERGR
• BIBLE BIBLER
• PRAY PRAYR
• WORSHIP WORSHIPR
• Examine frequency distributions for these to
  assess variance

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Index Construction

• 1. Item selection
• 2. Index scoring
• 3. Examination of empirical relationships
• 4. Handling missing data

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3. Examination of empirical relationships

• Generally, responses to index items should be
  related.
• E.g., in survey data, respondents who answered a
  certain way (e.g., LR) on one question should
  tend to answer the same way (LR) on others in the
  index.
• Examine all possible bivariate relationships
  among the index items to assess this (e.g., SPSS
  crosstabulation).

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• Possible results of bivariate analysis
• Two items have a moderate to strong to one
  another, but not a very strong/perfect
  relationship -gt Include both, since they probably
  measure slightly different aspects of the same
  concept.
• Two items are very strongly/perfectly related to
  one another -gt Include only one, since they
  probably measure a similar aspect of the same
  concept.
• Two items are only weakly related or not related
  to one another -gt Do not include both, since they
  probably do not measure the same concept.

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Gamma Values for Bivariate Relationships Between
Items
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Index Construction

• 1. Item selection
• 2. Index scoring
• 3. Examination of empirical relationships
• 4. Handling missing data

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4. Handling missing data

• If there are few cases with missing data on one
  or more items, the cases can be excluded from the
  index (e.g., Ch. 6 exercise).
• A value can be assigned to missing data according
  to some rule (e.g., mean of the variable, random
  assignment).
• If relatively few items have missing data for a
  case, an index score can be assigned to the case
  on the basis of the items with non-missing data.
• The structure of the data collection instrument
  may allow the researcher to impute responses
  (e.g., checking yes for some items on a list
  and leaving others blank blank probablyno).
• Analysis of other questions among those who had
  missing data may suggest probable answers to the
  missing ones.

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Creating the index
RELINDEX - Reliogisity Index
RELINDEXattendrclergrbiblerprayr
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Creating the index in SPSS

• In Data Editor window Transform Compute
• Type index name (8 characters or fewer first
  character must be alphabetic) in Target Variable
  box
• Highlight first variable in variable list and
  move to Numeric Expression box (or type in box)
• Type or use keypad to insert after first
  variable
• Continue until all variables have been entered
• Click TypeLabel and enter a variable label for
  your index under Label do nothing with Type
• Click OK to create the index and return to the
  Data Editor window (the index will be the last
  variable)
• Click Variable View and enter Value Labels for
  the index (e.g., 0-Lowest, 4-Highest)

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After index creation - Frequency distribution

• Run a frequency distribution in SPSS using the
  new index variable to assess one aspect of index
  scoring Range of measurement vs. adequate number
  of cases at each point.
• Both should be adequate, but it is not possible
  to define this precisely.
• In general, the index should have a sufficiently
  broad range of measurement to distinguish
  extremes of the concept.
• However, there should be sufficient
  representation of cases at each point, and no one
  point should have an extremely large number of
  cases.

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Index validation

• From Ch. 5 Validity - Does the measurement
  technique reflect the nominal definition?
• Aspects of validity in index construction and
  use
• 1. Internal validation - Item analysis
• 2. External validation

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1. Internal validation - Item analysis

• Examine the relationship the composite index
  variable and each individual item
• E.g. in SPSS Crosstabulate ATTENDR, CLERGR, etc.
  with RELINDEX
• Here, the index (RELINDEX) is the column variable
  and the item (ATTENDR) is the row variable, but
  it could be done the other way around.
• If the index is fairly strongly related to each
  item, we have support for internal validation.
• If not, reconsider item selection

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Example of Internal Validation
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2. External validation

• The index variable should be related to another
  variable measuring the same or a similar concept
• E.g., an index of religiosity should be related
  to
• belief that the U.S. would be a better country if
  religion had less influence (RELIGINF-not in GSS
  2000)
• place of faith in God in respondents value
  structure (IMPGOD-not in GSS 2000)
• whether somebody who is against all churches and
  religion should be allowed to teach in a college
  or university (COLATH-in GSS 2000)
• If not, either the index is a poor measure of the
  concept or the other variable (the validating
  item) is a poor measure of the concept.

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Example of External Validation
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Index and scale construction logic
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How indexes and scales are different

• If we know a respondents index score, we cant
  tell how individual items in the index were
  answered, unless the score is at one of the two
  extremes.
• Index scores are assigned by simply summing
  scores to the individual items.
• RELINDEX - 4 items, where 0all LR 4all HR
• But if RELINDEX1, we dont know which one was
  HR. If RELINDEX2, we dont know which two were
  HR. Same for 3.
• If items form a scale, knowing a respondents
  scale score, will tell us how each individual
  item was answered.
• Scale scores are assigned to ideal patterns of
  attributes.
• Data analysis determines whether items form a
  scale in a particular sample.

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Index and scale construction logic
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How indexes and scales are similar

• Both are composite measures (more than one item).
• Both rank cases from low to high with regard to
  the concept (ordinal).

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The End