1. Scales & Indices

2. 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

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

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

12. 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

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

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

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

16. 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

17. Combining items into a scale
Summative scale
Factor scores

18. 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

19. 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

20. 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

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

22. 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