Scales and Indices

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Scales and Indices
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While trying to capture the complexity of a
phenomenon

• We try to seek multiple indicators, regardless of
  the methodology we use
• Qualitative we prepare a sequence of questions
  and then ask more questions that help us clarify
  the issue of investigation
• Quantitative we construct several questionnaire
  items that help identify the concept

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Composite Measures

• In quantitative research are the
• Sequence of items that
• Target the same issue
• Within the same questionnaire
• To achieve a fuller representation of the concept
  under investigation

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Index

• Babbie (2004, p. 152)
• A type of composite measure that summarizes and
  rank-orders several specific observations and
  represents some more general dimensions
• In other words it combines several distinct
  indicators of a construct into a single score ?
  generally is a sum of scores of such indicators

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Index

• Example a) your first exam contained 67
  objective multiple-choice questions. The number
  of correct answers you received is the index of
  your understanding of the subject.
• b) your first project in this class has a
  checklist of issues to be addressed while you are
  working on it. The number of checkmarks you make
  on it once completing the project is your index
  of how ready it is for submission.

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Index

• Neuman (2000, p. 177) Base your answers on your
  thoughts regarding the following four
  occupations long-distance truck driver, medical
  doctor, accountant, telephone operator. Score
  each answer 1 for yes and 0 for no
• 1. Does it pay a good salary?
• 2. Is the job secure from lay-offs
• 3. Is the work interesting and challenging?
• 4. Are its working conditions good?
• 5. Are there opportunities for career
  advancement?
• 6. Is it prestigious or looked up to by others?
• 7. Does it permit freedom in decision-making?

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Index Construction

• Establish the face validity ?
• - Do your items pertain to the population?
• - Are your items general or specific?
• - Do the items provide enough variance?
• Examine bivariate relationships (logical
  consistency between all items)
• Examine multivariate relationships
  (correspondence between one group of items
  measuring the same thing and another group of
  items measuring the same thing)

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Index Scoring

• What is your measurement range?
• Is there an adequate number of cases for each
  index point?
• Is there a need to assign weights to items?
• If unweighted, each of your items has the same
  value for the concept, so ? sum up
• Weighting changes the theoretical definition
  of the construct, as some items matter more than
  others

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Scale

• Babbie (2004, p. 152)
• A type of composite measure composed of several
  items that have a logical or empirical structure
  among them
• In other words allows to measure the intensity
  or direction of a construct by aligning the
  responses on a continuum

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Scale

• Exist in a variety of types
• Five most widely known are
• - Likert scale
• - Bogardus Social Distance scale
• - Thurstone scale
• - Guttman scale
• - Semantic Differential scale

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Likert Scale

• Neuman (2000, p. 183)
• Neuman (2000, p. 183)

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Semantic Differential Scale

• Babbie (2004, p. 171)

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Bogardus Social Distance Scale

• This social distance scale was taken from
  http//garnet.acns.fsu.edu/jreynold/bogardus.pdf

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Guttman Scale

• Neuman (2002, p. 191)

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Thurstone Scale

• Neuman (2000, p. 187)

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Scale Scoring

• Response frequencies could be used to identify
  the intensity (direction, potency, etc.) of a
  construct
• Often, if several scales are used to identify a
  construct, the responses are summed and averaged
  in order to receive an index.

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Validation

• Internal validation
• Item analysis An assessment of whether each
  of the items included in a composite measure
  makes an independent contribution or merely
  duplicates the contribution of other items in the
  measure (Babbie, 2004, p. 164)
• Is conducted through a variety of statistical
  techniques
• - Regression
• - Factor Analysis

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Validation

• External validation
• The process of testing the validity of a
  measure by examining its relationship to other
  presumed indicators of the same variables
  (Babbie, 2004, p. 165)
• Is conducted by
• - trying it on a population with apparent traits
• - statistical procedures of establishing
  concurrent and predictive validity (often
  simple correlations)

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Bad Index vs. Bad Validators

• Fails the Internal Validation
• Item analysis can show presence of inconsistent
  relationships between the items
• Item analysis can show that the contribution of
  an item is insufficient
• The overall model is not supported by the data
  you collected
• Generally means that you need to either go
  back and re-think your theory or look for more
  relationships between the items in your model

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Bad Index vs. Bad Validators

• Fails the External Validation
• The index does not adequately measure the
  variable in question
• The validation items do not adequately measure
  the variable ? thus, do not provide a sufficient
  testing power
• Generally means that you need to go back and
  re-examine you measure before blaming it on the
  validators

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Missing Data

• Try to guess from previous responses what value
  to insert (not a good idea)
• Substitute the average score for cases where data
  are present (creates threats to validity)
• Eliminate all cases for which any information is
  missing (reduces the size of the usable data)

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Sampling
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Non Probability

• Do not know the size of the population from which
  the sample was drawn.
• Therefore, do not know how representative are
  their responses, controlling for their
  social-demographic characteristics.

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Non Probability

• Purposive
• Snowball
• Quota
• Selected Informants

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Probability

• Do know the size of the population from which the
  sample was drawn.
• Do know how representative are their responses,
  controlling for their social-demographic
  characteristics.

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Probability

• Simple Random
• Systematic
• Stratified
• Multistage
• Probability Proportionate to Size
• Disproportionate with Weighting

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Probability

• Bias Effect of theoretically relevant
  characteristics on responses.
• Population, Study Population, Sampling Frame,
  Sampling Unit
• Sampling Error