Factor Analysis
In many real-world datasets, we collect a large number of related variables.
Analyzing each variable separately can be confusing and inefficient.
Factor Analysis is a technique used to reduce many variables into a smaller set of underlying factors while preserving most of the information.
Why Factor Analysis Is Needed
Consider a survey measuring job satisfaction with questions on:
- Work environment
- Salary satisfaction
- Relationship with manager
- Career growth
- Recognition
These variables are related. Factor analysis helps identify hidden dimensions such as:
- Work Conditions
- Compensation
- Career Development
This simplifies analysis and interpretation.
Key Idea Behind Factor Analysis
Factor analysis assumes that:
- Observed variables are correlated
- Correlations are caused by underlying factors
Each factor represents a latent (unobserved) construct.
The goal is to:
- Reduce dimensionality
- Identify structure in data
- Create interpretable factors
Types of Factor Analysis
Two commonly used approaches are:
- Exploratory Factor Analysis (EFA)
- Confirmatory Factor Analysis (CFA)
SPSS mainly supports Exploratory Factor Analysis.
Assumptions and Requirements
Before running factor analysis:
- Variables should be correlated
- Sample size should be adequate
- Data should be approximately normal
SPSS provides tests to check these conditions.
KMO and Bartlett’s Test
Two important diagnostics are:
- KMO (Kaiser-Meyer-Olkin)
- Bartlett’s Test of Sphericity
Interpretation:
- KMO > 0.6 → acceptable
- Bartlett’s test p < 0.05 → suitable for factor analysis
Example Dataset
Suppose we measure employee satisfaction using the following variables:
| Employee_ID | Salary | Work_Life | Growth | Manager | Recognition |
|---|---|---|---|---|---|
| 3101 | 4 | 5 | 4 | 5 | 4 |
| 3102 | 3 | 4 | 3 | 4 | 3 |
Factor analysis can group these into fewer meaningful factors.
Running Factor Analysis (Menu)
To perform factor analysis in SPSS:
- Go to Analyze → Dimension Reduction → Factor
- Select variables to analyze
- Check KMO and Bartlett’s test
- Choose extraction method (Principal Components)
- Select rotation (Varimax)
- Click OK
SPSS Syntax Example
FACTOR
/VARIABLES Salary Work_Life Growth Manager Recognition
/MISSING LISTWISE
/ANALYSIS Salary Work_Life Growth Manager Recognition
/PRINT KMO
/CRITERIA FACTORS(2)
/ROTATION VARIMAX.
Interpreting Factor Loadings
Factor loadings show how strongly a variable is associated with a factor.
Guidelines:
- Loadings > 0.5 are considered strong
- Each variable should load strongly on one factor
Based on loadings, factors are named meaningfully.
Common Mistakes
Typical errors include:
- Running factor analysis without checking KMO
- Extracting too many factors
- Poor factor naming
Interpretation matters more than computation.
Quiz 1
What is the goal of factor analysis?
To reduce many variables into fewer underlying factors.
Quiz 2
What does KMO measure?
Sampling adequacy.
Quiz 3
Which rotation improves interpretability?
Varimax rotation.
Quiz 4
What loading value is considered strong?
Greater than 0.5.
Quiz 5
Does SPSS mainly support EFA or CFA?
Exploratory Factor Analysis (EFA).
Mini Practice
Create a survey dataset with at least five related variables.
Run factor analysis and identify two meaningful factors.
Check KMO, extract factors, apply Varimax rotation, and name factors logically.
What’s Next
In the next lesson, you will learn about Principal Component Analysis (PCA) and how it differs from Factor Analysis.