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Indexes, Scales, and Typologies

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Title: Indexes, Scales, and Typologies


1
Chapter 6
  • Indexes, Scales, and Typologies

2
Two familiar indexes
  • Consumer Price Index
  • Dow Jones Industrial Average

3
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

4
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

5
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.

6
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.

7
Index Construction
  • 1. Item selection
  • 2. Index scoring
  • 3. Examination of empirical relationships
  • 4. Handling missing data

8
1. Item selection Criteria
  • (1) Face validity
  • (2) Unidimensionality
  • (3) Variance

9
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.

10
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).

11
  • 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.

12
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.

13
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)

14
Index Construction
  • 1. Item selection
  • 2. Index scoring
  • 3. Examination of empirical relationships
  • 4. Handling missing data

15
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

16
Item scoring - ATTEND
Low Religiosity (0)
High Religiosity (1)
17
Item scoring - CONCLERG
18
Item scoring - BIBLE
19
Item scoring - PRAY
20
Item scoring - WORSHIP
21
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

22
Index Construction
  • 1. Item selection
  • 2. Index scoring
  • 3. Examination of empirical relationships
  • 4. Handling missing data

23
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).

24
  • 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.

25
Gamma Values for Bivariate Relationships Between
Items
26
Index Construction
  • 1. Item selection
  • 2. Index scoring
  • 3. Examination of empirical relationships
  • 4. Handling missing data

27
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.

28
Creating the index
RELINDEX - Reliogisity Index
RELINDEXattendrclergrbiblerprayr
29
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)

30
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.

31
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

32
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

33
Example of Internal Validation
34
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.

35
Example of External Validation
36
Index and scale construction logic
37
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.

38
Index and scale construction logic
39
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).

40
The End
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