Chapter 10

Combining Indicators: Index Construction

Modified: 2008-03-26

• I. Index defined
  • A. Scale is same as an Index but...
  • B. Indices are typically a collection of scales
  • C Examples include:
    • CPI
    • NASDAQ
    • GPA
    • Uniform Crime Reports
  • Indices are usually more reliable measures than are single scales
• II. Defining the concept
  • A. Define and describe concept to be measured
    • Researcher must have a good operational definition for the concept to be measured
    • The conceptual definition and operational definition must be close
  • B. Conduct literature review
    A literature review will help define both conceptual and operational definitions
  • C. Operational definition
    • Be sure to specify how the concept will be measured
• III. Selecting the items
  • A. Associated with content validity
    • Don't use items that do not show content validity
  • B. Use the right items
    • Items used should ONLY reflect the item of interest
  • C. Include enough items
    • Reliability increases as the number of items increases
  • D. Decide if item represents entire dimension or part
    • Some items will measure the concept globally, while others will only measure a part of the concept
    • For example, the ACT Composite provides a global measurement
  • E. Exclude items which provide no extra information
    • Don't add items willy-nilly. If an item does not provide additional information, don't use it
    • Be sure that items chosen are representative of concept (e.g., job performance)
    • Unrepresentative items will bias the index
    • Choose items by yourself or in conjunction with others
    • Look for items that "hang together"
    • Use factor analysis (see below) to find items that cluster together mathematically
• IV. Combining the items
  • A. Additive
    • The items are added together to create the index
    • The City Stress Index added: alcoholism, divorce, suicide, and crime
  • B. Average
    • All items are averaged together to create the index
  • C. Transformation
    • Some indeces use more complicated mathematical formulas and some transform scores before applying the formula
    • Both absolute and relative standards can be used for indeces
• V. Weighting the separate items
  • A. Relative importance
    • Indeces may weight all items equally or
    • Indeces may weight items differently
    • In either case, the validity of the index should be checked
• VI. Creating standardized indicators
  • A. Comparable units and contributes appropriately to composite measure
    • Standardizing means to put each variable to the same scale (e.g., Z scores)
    • Standardizing from 0 to 100 is typical
  • B. Issues
    • Standardization can also be accompanied by combining, transforming, or weighting
• VII. Examples of creating indices
  • A. Likert scaling
    • The most common format for tests that measure respondent's attitudes is a Likert scale (named after its developer, Rensis Likert). A Likert scale presents an item and a range of responses such as strongly disagree, disagree, no opinion, agree , and strongly agree . A respondent simply checks the response that is closest to his or her attitude.
    • Likert scales commonly use 5, 7, or 9 responses
    • Some items can be reverse scored. The advantage of reverse scoring is that it helps break up a respondent's mental set. That is, after two or three items in which a respondent checks strongly agree ( or disagree) , there is a tendency to continue to check the same response. An item that is reversed scored encourages a closer reading by the respondent.
    • Often, scales exclude the middle value
    • Treating the choices as interval data points allows for chi-square, t-tests, and ANOVA
• VIII. Factor analysis
  • A. Purpose and use
    • 1. Investigate relationship between concepts and indicators
    • 2. Assist in constructing indicators of abstract concepts
    • 3. Condense a large numbers of measures
      • The condensed set of measures is more reliable
  • B. Procedures
    • 1. Maximization of association
    • 2. Factor loadings
      • Range from 0 to 1
      • Loadings closer to 1 indicate closer associations
      • Associations are mathematical
      • Researchers "name" the loadings found
    • 3. Level of measurement
      • Interval level measurement is necessary
    • 4. Large number of cases necessary
      • Higher N provides greater reliability
• IX. Index numbers
  • A. Defined
    • Index numbers show changes over time from a specified value to a base value
  • B. CPI
    • CPI Calculator
    • The CPI allows researchers to compare amounts spent over time adjusted for inflation
• X. Chapter summary

Web Pages

Likert Scaling on Google

Factor Analysis on Google

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