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Scales & Indices

Scales & Indices. Measurement Overview. Using multiple indicators to create variables Two-step process: 1. Which items go together to measure which variables Factor Analysis 2. Evaluating the reliability of multi-item scales Cronbach’s Alpha. Factor Analysis.

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Scales & Indices

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  1. Scales & Indices

  2. MeasurementOverview • Using multiple indicators to create variables • Two-step process: • 1. Which items go together to measure which variables • Factor Analysis • 2. Evaluating the reliability of multi-item scales • Cronbach’s Alpha

  3. Factor Analysis • Starts with a group of similar indicators (survey items) • Sorts items based on patterns of inter-item similarities • I.e., which items are correlated (which ones group together) • Items that group together share some underlying common underlying factor • Procedure is based on inter-item correlations • Correlation: • Measure of similarity between two variables • Varies between 1 and -1

  4. Stages in Factor Analysis • Extraction • How the computer searches for patterns • Rotation • Mathematical manipulation of patterns • Whether the computer produces correlated or uncorrelated factors

  5. Concept measurement example: • Research on effects of TV news coverage of social protest • Subjects shown one of three TV news stories about an anarchist protest: • 1. Extremely critical • 2. Highly critical • 3. Moderately critical • Respond to questionnaire • Examined differences between exposure groups

  6. Example of Factor Analysis • Started with 28 items measuring attitudes • Factor analysis reduces to underlying factors…

  7. Remove

  8. Remove

  9. Remove

  10. Five Factors • 1. Protest rights • 2. Police hostility • 3. Protest utility • 4. Blame the protesters • 5. Anti-violence

  11. 1. Support for Protest Rights • A. Protesters have a right to protest • B. Protesters should not be allowed to protest in public places (reverse coded) • C. Protesters have a right to be heard

  12. 2. Hostility the Police • A. Police were out of line • B. Police used excessive force • C. Police were violent

  13. 3. Utility of Protest • A. Protesters offer new insights • B. It’s important to listen to protesters • C. Protesters brought issues to my attention

  14. 4. Blame the Protesters • A. Protesters initiated the conflict • B. The protesters were disrespectful • C. Protest was ineffective on politicians

  15. 5. Opposition to Protest Violence • A. I feel sorry for the police because of the way they were treated by the protesters • B. The protesters were violent

  16. Combining items into a scale • Summative scale • Factor scores

  17. Summative scales • Adding items or taking the mean • E.g.,: • Compute scale = sum.1(var1,var2,var3) • Compute scale = mean.1(var1,var2,var3) • Weights each item equally

  18. Factor scores • Uses factor loadings from the factor matrix to weight the items • Heavier weighting to items that are more central to the factor • Use save command when running factor analysis (under “scores”: “save as variables” • New variables with values for each case saved in data file for each factor

  19. Cronbach’s Alpha • Assessing reliability of a multi-item scale • Based on the average inter-item correlation • Weighted by the number of items in the scale • Measures internal consistency (unidimensionality) • Are all the items measuring the same thing? • If so, they should all be highly inter-correlated

  20. Cronbach’s Alpha Formula: A = N * r [1+ (N –1)r] N = number of items in the scale r = average inter-item correlation

  21. Acceptable alpha for a scale • Ideally, alpha > .80 • Some journals accept > .70 • Low alpha means either: • 1. Scale is not reliable (items have lots of error) • 2. Items could measure two different things • Alpha if item deleted can help identify a bad item • More than one bad item could be an indicator that there are items that measure a different concept

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