Mastering PCA with SPSS: Step‑by‑Step Guide to Data Reduction

Introduction to Principal Component Analysis

PCA is a common dimensionality‑reduction technique that finds the most important directions of variance in data, allowing fewer features to describe the data while preserving its essential structure.

General Steps of PCA

Select initial variables based on the research question.

Check suitability with KMO and Bartlett’s tests.

Standardize and normalize variables (e.g., max‑min, z‑score) and ensure consistent direction.

Compute the correlation matrix.

Obtain eigenvalues and eigenvectors of the covariance matrix.

Determine component expressions, select the number of components, and compute scores.

Interpret components in relation to the original variables.

Key relationships: each component is a linear combination of original variables, the number of components is less than the number of variables, components retain most information, and components are orthogonal.

SPSS Procedure

Problem and Data

某公司经理拟招聘一名员工，要求其具有较高的工作积极性、自主性、热情和责任感。为此，该经理专门设计了一个测试问卷，配有25项相关问题，拟从300位应聘者中寻找出最合适的候选人。在这25项相关问题中，Q3‑Q8、Q12、Q13测量的是工作积极性，Q2、Q14‑Q19测量的是工作自主性，Q20‑Q25测量的是工作热情，Q1、Q9‑Q11测量的是工作责任感，每一个问题都有1‑7等级。该经理想根据这25项问题判断应聘者在四个方面的能力，现收集了应聘者的问卷信息，经汇总整理后部分数据如图1。

Assumption 2: Linear Correlation

The correlation matrix (25×25) shows coefficients ≥0.3 within each group, confirming linear relationships.

KMO and Bartlett Tests

KMO overall = 0.828 (good), individual KMO > 0.7, Bartlett’s test p < 0.001, indicating suitability for PCA.

Result Interpretation

Communalities

All variables explain 100 % of variance when all components are retained; after selecting components, explained variance decreases.

Extracted Components

Eigenvalues and variance explained: PC1 = 6.517 (26.07 %), PC2 = 3.456 (13.82 %), PC3 = 2.962 (11.85 %), PC4 = 1.912 (7.65 %). Four components are recommended based on eigenvalue > 1, cumulative variance (~59 %), scree plot, and interpretability.

Rotated Component Matrix

After varimax rotation, the four components correspond to work enthusiasm, autonomy, passion, and responsibility, matching the questionnaire design.

Forcing a Four‑Component Solution

In SPSS, set “Fixed number of factors” to 4 and re‑run the analysis; the cumulative variance remains 59.386 %.

Conclusion

The study of 315 applicants shows that the data meet PCA assumptions, and the first four components explain 59.386 % of variance, reflecting the four targeted work‑ability dimensions.