Factor Analysis

Question 1

What is a factor analysis?

Answer 1

the values of observed data are expressed as functions of a number of possible causes in order to find which are the most important

Question 2

What is factor rotation?

Answer 2

a process by which we simplify the structure that we have

Question 3

What do we need eigenvectors and eigenvalues for?

Answer 3

Allows us to make calls about the structure - a structural element that represents the factors that allow us to make judgements

Question 4

What is factor loading?

Answer 4

Shows us how the individual elements relate to that structure and to those factors

Question 5

What elements do we need for a factor analysis?

Answer 5

• Principle component analysis (including factor rotation)
• Eigenvector and values
• Factor loadings

Question 6

What is a principle component analysis?

Answer 6

• How we are going to extract the data
• Takes a cloud of data points and finds the ‘principle axes’ of that cloud
• Lets you find the factors in factor analysis

Question 7

What does a principle component analysis produce?

Answer 7

Eigenvectors and associated eigenvalues

Question 8

What are eigenvectors?

Answer 8

Essentially our factors - mathematical foundation of the factors/components

Question 9

How do we interpret eigenvectors?

Answer 9

• Each has an associated eigenvalue that tells you how important it is
• Factors with high eigenvalues are important

Question 10

What is Kaiser’s Extraction?

Answer 10

• Used to tell which factors are important

- Retain factors with Eigenvalues > 1

Question 11

How do we use scree plots to tell which factors are important?

Answer 11

Use the ‘point of inflexion’

- Factors above this point are important and we keep and the ones below are unimportant

Question 12

What types of factor rotation are there?

Answer 12

• Orthogonal

- Oblique

Question 13

What is orthogonal factor rotation?

Answer 13

The factors are uncorrelated

Question 14

What is oblique factor rotation?

Answer 14

Factors inter-correlate

Question 15

How do we interpret factor loadings?

Answer 15

• Between 0 - 1
• High loadings are above 0.5
• Above 0.3 is interesting
• Can be + or - depending on the nature of the relationship to the element

Question 16

Can individual elements load on more than one factor?

Answer 16

Yes, but can be tricky to interpret

Question 17

What assumptions need to be met for a factor analysis?

Answer 17

• Variables need to be correlated together (r>.3)
• But not too correlated (multicollinearity is an issue)
• Avoid singularity
• Sphericity

Question 18

What is the use of Bartlett’s Test of Sphericity?

Answer 18

Testing to see if there are correlations between the variables

Question 19

What are the sample size requirements for the data?

Answer 19

• 100 is low
• 300 is good
• 1000 is great
• Minimum 2 PPs per variables

Question 20

What test can determine how good your sample size is?

Answer 20

Kaiser-Meyer-Olkin

- Should be above 0.5 to be adequate

Question 21

What methods can we use to test reliability?

Answer 21

• Test-retest method
• Split-Half Method
• Cronbach’s Alpha

Question 22

Explain the test-retest method

Answer 22

Test once and then test later after a certain time

Question 23

What is the split-half method?

Answer 23

Splits the questionnaire into two random halves, calculates scores and correlates them

Question 24

What is a disadvantage of the test-retest method?

Answer 24

Doesn’t always work as once the PP has been tested they may not be able to be tested again as they are not as naïve and will know the aim of the test (practice effect)

Question 25

What is cronbach’s alpha?

Answer 25

Splits the questionnaire into all the possible halves, calculates the scores, correlates them and averages the correlation for all splits
- Ranges from 0 (no reliability) to 1 (complete reliability)

Question 26

What are factor scores?

Answer 26

• You can get scores for each factor for each participant

- calculated by a combination of the factor loadings and the actual scores