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Reliability

Exploratory Factor Analysis — KMO, Eigenvalues, Loadings

Does a 6-item job satisfaction scale measure one thing or two? KMO=.744, Bartlett chi2(15)=555.13, Kaiser-rule eigenvalues, and a varimax-rotated clean 2-factor solution.

📊 KMO=.744, 2 factors, 75.1% variance explained
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🔬 35 · Exploratory Factor Analysis — KMO, Eigenvalues, Loadings

Does a 6-Item Job Satisfaction Scale Measure One Thing or Two?
Reliability
Research Question: 220 employees answered 6 Likert items intended to measure job satisfaction: three about pay (P1–P3) and three about coworkers (C1–C3). Do they really form two separate underlying factors, or one general factor? As is standard practice for an EFA worked example, we start directly from the item correlation matrix (below) rather than 220 raw rows.
P1P2P3C1C2C3
P11.00.65.62.20.18.22
P2.651.00.68.15.20.17
P3.62.681.00.22.19.21
C1.20.15.221.00.64.60
C2.18.20.19.641.00.66
C3.22.17.21.60.661.00
Kaiser-Meyer-Olkin (per item i and overall) and Bartlett's test of sphericity
K M O i = ∑ j ≠ i r i j 2 ∑ j ≠ i r i j 2 + ∑ j ≠ i a i j 2 , χ B a r t l e t t 2 = − [ ( N − 1 ) − 2 p + 5 6 ] ln ⁡ | R |
  1. 1
    Check the two gatekeeper tests before extracting anything:
    K M O o v e r a l l = .744   ( items  .708 – .780 ) χ B a r t l e t t 2 ( 15 ) = 555.13 ,   p < .001
    KMO=.744 is in the 'middling' range (Kaiser's guideline: >.60 acceptable, >.80 good) — adequate to proceed. Bartlett's test rejects the null that R is an identity matrix, confirming the items are correlated enough to factor.
  2. 2
    Extract eigenvalues of the correlation matrix (principal-component extraction, the default in most software):
    λ : 2.864 ,   1.705 ,   0.410 ,   0.390 ,   0.353 ,   0.278 ( ∑ λ = 6 )
    By Kaiser's rule (retain λ>1), exactly TWO factors survive — 2.864 and 1.705 — explaining 47.7% and 28.4% of variance (75.1% combined). The other four eigenvalues (all <1) are noise.
  3. 3
    Rotate with varimax for an interpretable simple structure:
    ItemFactor 1 (Coworker)Factor 2 (Pay)h²
    P1.124.853.742
    P2.082.887.793
    P3.130.866.766
    C1.851.109.735
    C2.878.105.781
    C3.858.121.750
    Clean simple structure: every item loads ≥.85 on its intended factor and ≤.13 on the other. Pay and Coworker satisfaction are empirically separate factors, not one general job-satisfaction factor.
  4. 4
    Decision rule: Retain 2 factors, not 1. Score the scale as two subscales (Pay Satisfaction = P1+P2+P3, Coworker Satisfaction = C1+C2+C3) rather than a single total score.
.744
KMO
555.13
Bartlett χ²(15)
2
Factors retained
75.1%
Variance explained
🔴 Two-factor structure confirmed — KMO=.744, Bartlett χ²(15)=555.13, p<.001. Pay and Coworker satisfaction are distinct factors (all loadings ≥.85, cross-loadings ≤.13).
APA-7
An exploratory factor analysis (principal-component extraction, varimax rotation) was conducted on the 6-item scale. The data were suitable for factor analysis, KMO = .744, Bartlett's χ²(15) = 555.13, p < .001. Two factors with eigenvalues > 1 were retained, explaining 75.1% of total variance. Items loaded cleanly onto their intended factor (all λ ≥ .85) with negligible cross-loadings (all λ ≤ .13), supporting a Pay Satisfaction and Coworker Satisfaction two-factor structure.

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