If you’ve ever collected survey data using likert scale (e.g., “Strongly Disagree” → “Strongly Agree”), you might be wondering: Do my questions really measure what I think?

It’s here factor analysis enter. This is a statistical tool that checks whether your survey items are grouped into meaningful groups (called factor). For example, ten questions about “job satisfaction” can actually form two factors: career growth And work environment.

But to do factor analysis correctly, you need to understand it metric which tells you whether your model is good. This guide covers all the essentials, step by step.

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🔹 Step 1: Check Data Suitability

Before running factor analysis, you need to check that your data fits.

Metrics used:

• Kaiser-Meyer-Olkin (KMO) test.
  • Measuring sampling adequacy.
  • Threshold: ≥ 0.6 acceptable, ≥ 0.7 good, ≥ 0.8 good, ≥ 0.9 excellent.
• Bartlett’s Test of Sphericity
  • Test whether your variables are sufficiently correlated.
  • Threshold: p < 0.05 (significant = suitable for factor analysis).

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Step 2: Extract Factors

Now, the software will start grouping items. But how many factors should you keep in mind?

Metrics used:

• Eigenvalues
  • Reflects the variance explained by each factor.
  • Threshold: Retain factors with eigenvalues ​​> 1 (Kaiser’s rule).
• Screen Plot
  • Visual inspection: look for the “elbow” point where the slope flattens out. Keep the factor before the elbow.
• Parallel Analysis (stronger)
  • Comparing actual eigenvalues ​​with eigenvalues ​​from random data. Keep factors above random limits.

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Step 3: Assess Factor Loadings

Factor loadings indicate how strongly each question is related to its factor.

Threshold:

• ≥ 0.30 → minimum
• ≥ 0.40 → acceptable
• ≥ 0.50 → good
• ≥ 0.70 → very strong

If an item has a low loading (<0.4) or loads on multiple factors (cross-loading), consider revising or deleting it.

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Step 4: Improve Interpretability with Rotation

Rotation makes your factor solution easier to read.

• Varimax (orthogonal): Use when the factors are independent.
• Oblimin/Promax (italics): Use if factors are correlated (common in social sciences).

Clean interpretation threshold: Each item must have a high loading on one factor and a low loading on another factor.

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Step 5: Check Reliability

Once the factors are identified, test whether they are reliable.

Metrics used:

• Cronbach’s Alpha
  • Checking internal consistency.
  • Threshold: ≥ 0.7 acceptable, ≥ 0.8 good, ≥ 0.9 excellent.
• Composite Reliability (CR)
  • More accurate in CFA.
  • Threshold: ≥ 0.7 is good.

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Step 6: Assess Validity

In addition to reliability, you need to ensure the construction is valid.

• Convergent Validity
  • Items measuring the same construct should be strongly correlated.
  • Measured using Average Variance Extracted (AVE).
  • Threshold: AVE ≥ 0.5.
• Discriminant Validity
  • Constructions must be different from each other.
  • Check whether square root of AVE > correlation with other constructs.
• Suitable Models (for CFA/SEM):
  • χ²/df (Chi-square/df): <3 great.
  • RMSEA (Root Mean Square Error of Approximation): < 0.08 is acceptable, < 0.05 is excellent.
  • Finance (Comparative Suitability Index): ≥ 0.90 good, ≥ 0.95 very good.
  • TLI (Tucker-Lewis Index): ≥ 0.90 good, ≥ 0.95 very good.
  • SRMR (Standardized Root Mean Square Residual): < 0.08 is acceptable.

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Final Checklist

Is a quick cheat sheet for factor analysis on Likert scale data:

1. SME ≥ 0.6 → Sample adequacy.
2. Bartlett’s test p <0.05 → Data matches.
3. Eigenvalue > 1 & Scree Plot → Retention factor.
4. Factor Loading ≥ 0.4 → Save powerful items.
5. Cronbach’s alpha ≥ 0.7 → Reliability check.
6. AVE ≥ 0.5, CR ≥ 0.7 → Convergent validity.
7. The square root of the correlation AVE > → Discriminant validity.
8. Finance/TLI ≥ 0.90, RMSEA < 0.08 → The model fits.

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Final Thoughts

Factor analysis helps you turn messy Likert scale responses into messy responses clear and validated constructs you can believe it. The key is not just to carry out analysis, but also check metrics carefully.

In short:

• First, make sure your data matches (KMO, Bartlett).
• Then, extract and refine the factors (eigenvalues, loadings, rotations).
• Finally, test reliability and validity (Alpha, AVE, CR, CFI, RMSEA).

Do all that, and your survey will have a solid statistical foundation—ready to be published or reported professionally.