What Is Principal Component Analysis? How to Read PCA in SPSS

What Is Principal Component Analysis

Principal Component Analysis, usually abbreviated as PCA, is a technique that transforms multiple correlated observed variables into a smaller number of principal components. When your questionnaire contains many observed variables, PCA helps summarize the information and identify groups of variables that tend to vary together.

In SPSS, PCA commonly appears within the Exploratory Factor Analysis process, or EFA. You enter the observed variables, select Principal Components as the extraction method, and then review KMO and Bartlett's Test, Total Variance Explained, and Rotated Component Matrix. Each component is created from a linear combination of the observed variables, with weights showing the contribution of each variable.

You need to make one distinction at the start. PCA focuses on summarizing the total variance of the variables, whereas some other factor extraction methods focus on the common variance shared by the variables. In many economics, management, and marketing theses, PCA is still selected when exploring scale structure. State the extraction method you used instead of writing only that you “ran EFA.”

If you are looking at the results and do not know where to start, see the guide to EFA in SPSS. This article focuses on understanding PCA, the thresholds commonly used, and how to decide which items should remain.

Why Principal Component Analysis Matters in Quantitative Research

PCA answers a practical question: how many meaningful groups can the observed variables in your questionnaire be reduced to for later analysis. For example, 20 original observed variables might be reduced to 4 components. Each component can then represent one aspect of the research construct.

In a thesis, PCA usually supports three decisions. First, you check whether the data are suitable for factor analysis. Second, you determine how many components to retain. Third, you examine which component each observed variable loads on most strongly and whether it cross-loads on several components.

PCA does not name the construct represented by a component. The factor name must come from the theoretical meaning of the observed variables grouped together. If three variables all describe the convenience of using a service, you might name the component “Convenience.” The software provides the numerical structure, while the interpretation must return to your study model and scale.

PCA results also do not replace the theoretical basis of the study. If your original model contains four constructs but PCA produces three groups, check why. Some variables may have similar content, the wording may be unclear, or the actual data may not support the expected structure. When you need to test an established structure, you can consider CFA, but CFA follows a different logic and should not be combined with PCA in the same conclusion.

What Counts as an Acceptable Principal Component Analysis Result

No single number determines whether the entire PCA is acceptable. Read a sequence of indicators in order: data suitability, number of components, total variance explained, factor loading, and cross-loading. The thresholds below are commonly used reference points, not permission to keep or remove items mechanically.

KMO indicates how suitable the overall correlations among the variables are for factor analysis. The lower the KMO, the more difficult it is for the data to produce a clear factor structure. Bartlett's Test checks whether the correlation matrix differs from an identity matrix. When Sig. is below 0.05, the variables are correlated enough to continue considering PCA.

Eigenvalue is the amount of variance explained by a component. The rule of an eigenvalue greater than 1 is commonly used by SPSS to suggest the number of components, following (Kaiser, 1960). Do not look at this number alone. Also review the Scree Plot and whether the variable groups make sense. A component with an eigenvalue that barely exceeds the threshold, only one variable, or no theoretical meaning needs careful review.

Factor loading shows the strength of the relationship between an observed variable and a component. A cutoff of 0.5 is commonly used in quantitative research, following (Hair et al., 2010). In an exploratory study, some guidelines may accept a lower cutoff, but you need to agree on the rule with your supervisor and explain it clearly in the thesis. A high cross-loading means that an item loads at nearly the same level on several components, which usually makes the factor name harder to justify.

How to Read Principal Component Analysis Output

Open SPSS and go to Analyze > Dimension Reduction > Factor. Move the observed variables you want to check into the Variables box. Under Extraction, set Method to Principal components, turn on Scree plot, and keep Eigenvalues over 1 if that is the rule you are using. Under Rotation, choose Varimax when you want the components to have low correlations. If your theoretical model allows correlated factors, you can consider an oblique rotation such as Direct Oblimin.

Under Descriptives, select KMO and Bartlett's test, Anti-image, and Correlation matrix if you need a deeper check. Under Options, you can select Sorted by size to make the factor-loading table easier to read and set Suppress small coefficients at an appropriate level. Hiding small coefficients makes the table more compact, but you still need to check how that setting affects your interpretation.

The table below is illustrative output, not the result of a specific study. The table name and columns follow simulated SPSS output so you can compare them with the file currently open on your computer.

Read the KMO and Bartlett's Test table first. In the example, KMO is 0.812 and Sig. is 0.000. This indicates that the data are suitable for continuing with PCA according to the thresholds described above.

Next, read Total Variance Explained. The Cumulative % column shows the total percentage of variance explained by the number of components being retained. In the example, four components explain 67.438% of the variance. This exceeds the 50% reference point in (Hair et al., 2010), but you still need to check whether those four components fit the research model.

Finally, open Rotated Component Matrix. Check which component has the highest loading for each item, whether that loading reaches your selected threshold, and whether the item has a meaningful loading on several components. Do not read one row in isolation and make an immediate decision. Create a list containing the item code, highest loading, second-highest loading, and the difference between those two values.

If this table is confusing, rotated matrix will help you focus on the correct columns and identify cross-loadings. Eigenvalue covers the separate decision about how many components to retain.

What to Do When Principal Component Analysis Does Not Meet the Thresholds

Work from the original data toward the model instead of deleting a batch of items to make the table look cleaner. First, check the data entry. A variable may have been entered with the wrong type, all responses may be identical, many values may be missing, or a reverse-coded item may not have been recoded. These problems distort the correlations between variables.

Check Correlations and Missing Data First

Review the Frequencies, Descriptives, and Correlations tables. If a variable has almost no variation, it is unlikely to contribute to forming a component. Also check the number of missing values and unusual response codes. If the questionnaire uses a Likert scale from 1 to 5 but the file contains 99, recode 99 as missing before running the analysis again.

Review Items with Low Factor Loadings

If an item has a loading below the threshold you selected, reread the item and check its Corrected Item-Total Correlation during the Cronbach's Alpha step. Removing the item may be reasonable when its statistical evidence is weak and it is not essential to the construct's content. Record which item was removed, at which run, and for what specific reason.

Deal with Cross-Loading

An item that loads highly on two components may have overlapping content or unclear wording. Check the difference between the two loadings, the number of remaining items in each component, and the theoretical meaning. Removing an item simply because it makes the rotated table look cleaner is weak justification. If you remove it, run PCA again and check KMO, explained variance, and the new structure.

Check the Number of Components Retained

If the eigenvalue greater than 1 rule produces too many small components that are difficult to name, review the Scree Plot, the number of items in each component, and the theoretical model. You can test a fixed number of components when there is a clear methodological reason, then compare how interpretable the results are. Record every change in a data-processing log so that you do not have to reconstruct the different runs when the committee asks about them.

Do not use PCA to force data to confirm a failed hypothesis. If the results remain unsuitable, the cause may be the scale, the survey sample, or the way the model was constructed. Software cannot repair an observed variable that does not measure the intended construct.

Distinguishing Principal Component Analysis from EFA, CFA, and Communality

PCA is a component extraction method. EFA is a broader exploratory process that includes selecting variables, choosing an extraction method, selecting a rotation, and interpreting the structure. Therefore, saying that “PCA and EFA are exactly the same” leaves out part of the method. In much SPSS output, PCA is used within the EFA process, but you should still report Extraction Method: Principal Component Analysis.

CFA tests a measurement structure that has already been specified. You enter the relationships between observed variables and latent variables into the model, then assess model fit and measurement validity. PCA and CFA have different purposes, so one does not directly replace the other.

Communality is the proportion of an observed variable's variance explained by the retained components. In SPSS, you will usually see Initial and Extraction in the Communalities table. To read this statistic correctly, see the guide to communality. Low communality may suggest that the components do not represent the item well, but the decision to remove the item still needs to consider its loading and the scale content.

You also need to distinguish PCA from regression analysis. PCA creates a summary structure from a group of correlated variables, while regression tests relationships between independent and dependent variables. You can use factor scores or mean scores after the measurement step to run regression, but the two steps answer different questions.

Common Errors

The first error is writing that “PCA is acceptable” simply because KMO is greater than 0.5. KMO only addresses initial suitability. You still need to read Bartlett's Test, the number of components, explained variance, loadings, and cross-loadings.

The second error is treating every loading above 0.5 as evidence that the scale is perfect. An item with a high loading may still cross-load, belong to the wrong theoretical group, or reduce the scale's internal consistency. Read the full rotated matrix, not only the cells printed in bold by SPSS.

The third error is repeatedly deleting items without saving each file version. Save the data file and output by run, such as PCA_v1 and PCA_v2, together with a record explaining why each item was removed. This lets you restore the results and explain the process transparently.

The fourth error is using CB-SEM thresholds to evaluate PCA. CFI, TLI, RMSEA, and SRMR belong to the assessment of model fit in CB-SEM, according to (Hu and Bentler, 1999), and they are not the main criteria for reading PCA in SPSS.

How to write this in your thesis

You can adapt the following sentence to your actual results: “The PCA results show that the KMO value was [KMO], while Bartlett's Test had Sig. = [Sig.], indicating that the data were suitable for factor analysis. [Number of factors] were retained, explaining [Cumulative %]% of the total variance, and the observed variables had factor loadings ranging from [lowest loading] to [highest loading].” Fill in the numbers only after checking them directly against the output, and state which items were removed, if any.

Frequently asked questions

What is Principal Component Analysis in SPSS?

Principal Component Analysis is a method for transforming a group of observed variables into a smaller number of components. In SPSS, PCA is commonly run through Analyze > Dimension Reduction > Factor and read through the KMO and Bartlett's Test, Total Variance Explained, and Rotated Component Matrix tables.

What counts as an acceptable PCA result?

You need to assess several criteria together. Common reference points are KMO of 0.5 or above, Bartlett's Test with Sig. below 0.05, eigenvalue greater than 1, total variance explained of 50% or above, and factor loading of 0.5 or above. The relevant sources are (Kaiser, 1974), (Kaiser, 1960), and (Hair et al., 2010).

What should I do when PCA has a low KMO?

Check for variables with low variance, missing data, incorrect codes, and weak correlations between variables. You can review the Anti-image table, but remove an item only when both statistical and content-based evidence support the decision. After each removal, run the full PCA again and record the changes in KMO, Bartlett's Test, and the factor structure.

Is PCA the same as EFA?

PCA is a component extraction method, while EFA is a broader process for exploring factor structure. In SPSS, PCA is often selected as the Extraction Method within the Factor Analysis procedure, so the two terms appear together but are not completely synonymous.

Do I need to run PCA before CFA?

That depends on the research design and the source of the scale. If you are exploring the structure of an adapted scale, PCA or EFA may be used at the exploratory stage. CFA is appropriate when you already have a measurement structure that needs to be tested. State the purpose of each step clearly and do not use PCA results as a substitute for CFA evidence.

Open the SPSS file again and check KMO and Bartlett's Test, Total Variance Explained, and Rotated Component Matrix in that order. Then save an output copy with the list of processed items. If you need to run PCA on your own .sav or .csv file and turn the component results into Chapter 4 text, see DoThesis M4 data analysis.