Step 2: Analysis Phase

Factor Extraction

Once you've confirmed your data is suitable via KMO & Bartlett’s Test, the next step is to uncover the hidden structures or "clusters" in your data.

Revealing Underlying Themes

What is it?

Factor extraction is the mathematical process of reducing many observed variables into a smaller number of latent (unobserved) factors. It explains the patterns of correlations among your survey items.

Many Variables → Few Factors

⚙️ Common Extraction Methods

PCA

Principal Components Analysis

Identifies components that account for maximum variance in the data.

Best For: Data reduction or creating index scores.

Recommended

PAF

Principal Axis Factoring

Focuses on shared/common variance only.

Best For: Uncovering latent constructs (Applied Linguistics theories).

ML

Maximum Likelihood

Assumes normal distribution; provides fit statistics.

Best For: Comparing models or running significance tests.

🔁 The Extraction Flow

Original Variables

Your raw survey data

Correlation Matrix

Calculating relationships

Factor Extraction

Choose method: PCA, PAF, or ML

Initial Solution

Unrotated factors ready for review

📊 PCA vs. PAF Comparison

Feature	PCA	PAF (Recommended)
Variance Used	Total Variance	Only Common/Shared
Role	Data Reduction	Finding Latent Traits
Resulting Scores	Good for indices/scoring	Used for structure

📝 How to run in SPSS

1

Navigate

Analyze → Dimension Reduction → Factor
2

Extraction Tab Settings

Method: Principal Components OR Principal Axis Factoring
3

Visuals

Tick "Scree plot" and "Unrotated factor solution".

Factor Analysis: Extraction

Method Selection:
[ ] Principal Components (PCA)
[x] Principal Axis Factoring (PAF) <-- Choose this for constructs!

Analyze:
[x] Correlation Matrix
[x] Scree Plot

Processing...
Extraction Complete.
Generating Output...

Instructor's Tip

"Start with PCA for basic exploration or index creation. However, use PAF if your goal is theoretical—to uncover hidden psychological traits or constructs in your research."