What Is PCA? How to Read and Process Principal Component Analysis Results

What Is PCA

PCA stands for Principal Component Analysis. It is also commonly called principal component analysis or principal component factor analysis. You use PCA when you have many observed variables and want to reduce them to a smaller number of components while retaining most of the information in the data's variation.

For example, your questionnaire may contain 20 observed variables measuring service quality. PCA may show that these 20 variables cluster into 4 components. Each component is a linear combination of the original variables. The software calculates the components from the variance in the data and the correlations between variables.

In SPSS, PCA appears within the Factor Analysis procedure. The menu path is Analyze > Dimension Reduction > Factor. In this dialog box, the Extraction section lets you choose Principal components. This is why many theses refer to the overall procedure as EFA even though the specific extraction method is PCA.

You can understand PCA through three main outputs. KMO and Bartlett's Test tells you whether the data are suitable for analysis. Total Variance Explained shows how many components are retained and what percentage of variance they explain. Rotated Component Matrix shows which component each observed variable loads on most strongly.

PCA does not prove that the components have theoretical meaning. You still need to compare the output with your research model, scales, and original hypotheses. If you need to review the concept of a scale before running the analysis, see what is a scale.

The Role of PCA in Quantitative Research

The first decision PCA supports is whether to retain or remove an observed variable. A variable with a low factor loading, substantial loadings on several components, or a position outside its theoretical group may need to be examined. Do not delete a variable just because one number looks unattractive. Review the item's content, the scale source, and the effect of removing it on the full model.

The second decision is identifying the initial structure of the dataset. If you expected the scale to contain 5 groups but PCA retains 3 components, that is a signal to investigate. Possible reasons include correlations that are too high between observed variables, wording that does not fit the Vietnamese context, an insufficient sample size, or a theoretical model that does not fit the data.

The third decision is creating representative variables for later analyses. After identifying the variable groups, you can calculate the mean score of the variables within the same component, or use factor scores depending on your research design. You can then enter these variables into regression, mediation, or moderation analysis. When your model includes a mediator, distinguish its role clearly from that of a moderator, as explained in the articles on mediation and moderation.

PCA is usually suitable when your goal is data reduction. In theses, many students use PCA to explore scale structure before running Cronbach's Alpha, regression, or PLS-SEM. The order of the procedures must be consistent with the method described in your methodology chapter. If you have used SmartPLS to assess the measurement model, do not bring CB-SEM fit indices into the PCA or PLS-SEM section.

PCA can also help detect problematic data, but it does not replace data cleaning. A few unusual observations can change the correlations between variables. Therefore, check outliers, missing data, reverse-coded variables, and responses that use the same rating for the entire questionnaire before interpreting PCA.

What Counts as an Acceptable PCA Result

No single number determines whether PCA is acceptable. Read the data suitability, number of components, total variance explained, and factor loadings together. The table below presents thresholds commonly cited in quantitative theses, with sources so you can explain your decisions.

These thresholds are reference points, not automatic permission to delete a variable. For a new or exploratory scale, Cronbach's Alpha from 0.6 may be accepted under (Hair et al., 2010), but that is a reliability criterion, not a direct PCA criterion. A Corrected Item-Total Correlation of 0.3 or above is associated with (Nunnally and Bernstein, 1994) and should also be reviewed during Reliability Analysis.

A KMO close to 0.5 only shows that the data are just adequate for consideration. A higher KMO generally indicates better suitability, but you still need to review Bartlett's test, communalities, factor loadings, and the theoretical structure. Total Variance Explained should not be used on its own to conclude that a scale is good.

How to Read PCA Output

Open Analyze > Dimension Reduction > Factor, move the observed variables into the Variables box, select Descriptives to obtain KMO and Bartlett's results, choose Extraction with Principal components, and then choose Rotation if you need the components to be easier to interpret. When the factor groups are likely to correlate, Promax is often more meaningful than Varimax. However, the rotation must match the method specified in your research proposal.

The table below is illustrative output, not the result of a real study. The column names follow the way SPSS usually displays them, so you can compare them with the file currently open on your screen.

First, review Kaiser-Meyer-Olkin Measure of Sampling Adequacy and the Sig. row in Bartlett's Test of Sphericity. If KMO is below 0.5 or Bartlett's test is not significant, do not read the rotated matrix as though the structure were already sound.

Next, open Total Variance Explained. The Initial Eigenvalues column shows the initial contribution of each component. The Cumulative % column shows the accumulated percentage of explained variance. If you retain 4 components, read the row for component 4, rather than only the percentage for the first component.

Then, inspect the Scree Plot. The bend in the plotted line helps you assess the number of components instead of mechanically retaining every component with an eigenvalue above 1. When the theoretical number of components differs from the number shown in the output, record the difference and inspect each variable.

Finally, read the Rotated Component Matrix. Each row is an observed variable, and each column is a component. Find the largest loading in each row, check whether it exceeds 0.5, and then check whether the variable also loads meaningfully on another column. After each variable-removal round, run PCA again and record the data version instead of deleting several variables at once without knowing which variable changed the result.

What to Do When PCA Does Not Meet the Criteria

If KMO is low, first check whether you accidentally included identification variables, demographic variables, or outcome variables in the PCA. PCA for a scale should use observed variables measuring the same conceptual group. Do not place age, gender, or respondent codes in the same analysis.

Next, check the correlation matrix and data quality. A variable that does not correlate with the rest can reduce suitability. You also need to check whether reverse-coded variables were recoded correctly. If a reverse-coded variable still has its original coding, its correlations may have the opposite sign and distort the structure.

If factor loading is low, read the item's content before removing it. A loading of 0.48 is not automatically grounds for removal in every study. You may consider removing the variable if its loading is low, it is not essential to the construct, and removing it improves the structure without eliminating an important part of the concept.

If one variable loads strongly on two components, you have a cross-loading. Review the difference between the two loadings, the wording, and the original theoretical group. Deleting a variable only to make the matrix look cleaner can leave the scale unable to cover the construct adequately. When you remove it, record the variable code, the reason, and the results before and after removal.

If Total Variance Explained is low, first check the number of components and the extraction method. Do not increase the number of components arbitrarily just to raise the explained-variance percentage. You can also review whether scales with different meanings were combined in one PCA. If the structure continues to fit poorly, discuss the measurement model and its presentation with your supervisor instead of editing the file until it crosses a threshold.

PCA rarely looks clean on the first run. Removing one variable, running the analysis again, and comparing the results is common. However, changing several options or deleting many unusual observations without a reason makes the analysis harder to defend.

PCA, EFA, and Principal Axis Factoring

PCA creates components from linear combinations of the total observed variance. Its main goal is reducing the number of dimensions. In SPSS, select this method under Extraction > Method > Principal components.

EFA, in the broad sense, is a procedure for exploring the structure of latent factors. EFA can use PCA, but it can also use Principal Axis Factoring, usually written as PAF. PAF focuses on the common variance shared by variables, whereas PCA handles total variance differently. The two methods can produce different numbers of factors or different loadings, especially when the scale contains substantial unique error.

Therefore, when writing your thesis, state both the name of the procedure and the extraction method accurately. The sentence “the study used EFA with PCA” is clearer than “the study ran EFA” when that is the actual SPSS selection. If your proposal requires PAF, do not change it to PCA simply because PCA produces an easier result.

PCA also differs from regression. PCA reduces variables and identifies correlation structures, whereas regression evaluates relationships between independent and dependent variables. PCA does not directly answer the hypothesis that X affects Y. It can create or confirm variable groups for use in a later analysis.

Common Errors

The first error is looking only at KMO and Bartlett's Test and then concluding that the scale is acceptable. KMO and Bartlett's test address the suitability of the data for analysis, not whether every variable has a good loading.

The second error is retaining components based on Eigenvalue > 1 without reviewing the Scree Plot or theory. This rule is a starting point associated with (Kaiser, 1960), but it should not replace methodological judgment.

The third error is reporting loadings without stating the rotation and extraction methods. Readers need to know whether you selected Principal components, Varimax, Promax, or another option.

The fourth error is deleting variables until the indices look good without saving each run. Use clear file names such as PCA_v1 and PCA_v2, and record the variable codes removed and the reasons. This lets you answer when your supervisor asks why the final structure differs from the original questionnaire.

The fifth error is confusing PCA with causal testing. If your goal is to test effects, you still need an appropriate model such as regression or PLS-SEM after PCA. If you are examining a moderator, see the article on moderation so you do not confuse scale-structure assessment with interaction testing.

Frequently asked questions

What is PCA and what is it used for?

PCA is Principal Component Analysis. It reduces many observed variables to a smaller number of components based on the correlation structure and variance of the data. In a thesis, PCA is often used to check whether observed variables group together in a way that fits the proposed model.

What counts as an acceptable PCA result?

Review KMO at 0.5 or above, Bartlett's Test with Sig. below 0.05, eigenvalues above 1, Total Variance Explained at 50% or above, and factor loadings at 0.5 or above. These reference points should be explained with (Kaiser, 1974), (Kaiser, 1960), and (Hair et al., 2010). No single index is sufficient to conclude that PCA is acceptable.

Is PCA the same as EFA?

PCA is an extraction method commonly selected within the EFA procedure in many theses. However, EFA can also use Principal Axis Factoring or another method. When reporting the results, state both the procedure and the extraction method selected in SPSS.

What should I do if PCA does not meet the criteria?

Check the variables entered, missing data, reverse-coded variables, identification variables, and response quality. Then review the correlation matrix, factor loadings, and cross-loadings before considering the removal of individual variables for a documented reason. Do not delete variables in bulk or change the method only to reach a threshold without recording the decision.

Do I need to run Cronbach's Alpha before PCA?

The order depends on the method design and your supervisor's requirements. Many studies run Cronbach's Alpha for preliminary screening and then run PCA or EFA to assess structure. If you remove a variable during Alpha, use the remaining set of variables when running PCA and report the processing rounds clearly.

Can PCA replace regression or SmartPLS?

PCA does not replace regression or SmartPLS. PCA focuses on variable structure and dimension reduction, whereas regression and PLS-SEM test relationships between variables in a model. You can use PCA results as a basis for processing scales before a later analysis when your research design allows it.

Open your SPSS file again and check KMO, Bartlett, Total Variance Explained, and Rotated Component Matrix in that order. Then save a version that records every variable you processed. If you need to run PCA on your own .sav or .csv file, use M4 data analysis.