2. Overview of Factor Analysis Construct combinations of quantitative variablesConstruct combinations of quantitative variables Reduce a large set of variables to a smaller number of factorsReduce a large set of variables to a smaller number of factors

3. Uses of Factor Analysis Develop and test theoriesDevelop and test theories Describe differences between individualsDescribe differences between individuals Determine which variables/measurements may be dropped from a scale or batteryDetermine which variables/measurements may be dropped from a scale or battery

4. Extraction of Factors Based on correlations among variablesBased on correlations among variables The first factor will explain the most variance in the original scores, with each factor explaining less varianceThe first factor will explain the most variance in the original scores, with each factor explaining less variance

5. Factor Rotation Transform the loadings to make it easier to interpret what the factors representTransform the loadings to make it easier to interpret what the factors represent A loading indicates how important a variable is for that particular factorA loading indicates how important a variable is for that particular factor VARIMAX is the most popular method:VARIMAX is the most popular method: –Maximizes variability in factor loadings within factors –Maintains orthogonal factors

6. Assumptions for Factor Analysis Linear relationships among variablesLinear relationships among variables Multivariate normal distributionsMultivariate normal distributions

7. Reporting Factor Analysis Decide on number of factors based on factor extraction (principal components analysis)Decide on number of factors based on factor extraction (principal components analysis) The eigenvalue for a factor represents the amount of variance in the original scores explained by the factorThe eigenvalue for a factor represents the amount of variance in the original scores explained by the factor Also look at percentage of variance explainedAlso look at percentage of variance explained

8. Reporting Factor Analysis One way to decide on the number of factors is to only use those with eigenvalues greater than oneOne way to decide on the number of factors is to only use those with eigenvalues greater than one The other way is to examine the scree plot and discard factors after the plot flattens out; this requires that you manually enter the number of factors you wantThe other way is to examine the scree plot and discard factors after the plot flattens out; this requires that you manually enter the number of factors you want

10. Reporting Factor Analysis Look at the rotated factor loadings to interpret and name the factorsLook at the rotated factor loadings to interpret and name the factors A confirmatory factor analysis can be done as a follow-upA confirmatory factor analysis can be done as a follow-up

11. Take-Home Point Factor Analysis can be used to reduce a large set of variables to a smaller number of factorsFactor Analysis can be used to reduce a large set of variables to a smaller number of factors