## Cramming Sam's top tips from chapter 18

Click on the topic to read Sam's tips from the book

### Preliminary analysis

• Scan the correlation matrix for variables that have very small correlations with most other variables, or correlate very highly (r = 0.9) with one or more other variables.
• In factor analysis, check that the determinant of this matrix is bigger than 0.00001; if it is then multicollinearity isn’t a problem. You don’t need to worry about this for principal component analysis.
• In the table labelled KMO and Bartlett’s Test the KMO statistic should be greater than 0.5 as a bare minimum; if it isn’t, collect more data. You should check the KMO statistic for individual variables by looking at the diagonal of the anti-image matrix. These values should also be above 0.5 (this is useful for identifying problematic variables if the overall KMO is unsatisfactory).
• Bartlett’s test of sphericity will usually be significant (the value of Sig. will be less than 0.05), if it’s not, you’ve got a disaster on your hands.

### Factor extraction

• To decide how many factors to extract, look at the table labelled Communalities and the column labelled Extraction. If these values are all 0.7 or above and you have less than 30 variables then the default (Kaiser’s criterion) for extracting factors is fine. Likewise, if your sample size exceeds 250 and the average of the communalities is 0.6 or greater. Alternatively, with 200 or more participants the scree plot can be used.
• Check the bottom of the table labelled Reproduced Correlations for the percentage of ‘nonredundant residuals with absolute values greater than 0.05’. This percentage should be less than 50% and the smaller it is, the better.

### Interpretation

• If you’ve conduced orthogonal rotation then look at the table labelled Rotated Factor Matrix. For each variable, note the factor/component for which the variable has the highest loading (above about 0.3–0.4 when you ignore the plus or minus sign). Try to make sense of what the factors represent by looking for common themes in the items that load highly on the same factor.
• If you’ve conducted oblique rotation then do the same as above but for the Pattern Matrix. Double-check what you find by doing the same for the Structure Matrix.