What Is Exploratory Factor Analysis? How to Read EFA in SPSS
What Is Exploratory Factor Analysis
Exploratory Factor Analysis, abbreviated as EFA, is used to examine how the observed variables in your questionnaire group into factors. You use EFA when your measurement model contains many observed variables and you want to see whether the actual structure of the data fits the concepts you expected.
For example, you may have 20 observed variables measuring service quality, trust, convenience and intention to continue using a service. EFA examines which variables vary together, which variables load strongly on the same factor, which variables load on more than one factor, and which variables fail to represent any group clearly.
EFA does not directly test a hypothesis such as “service quality affects purchase intention.” It deals with the measurement scale first, helping you identify the factor structure before you continue with Cronbach's Alpha, regression or a PLS-SEM model. In the common SPSS procedure, EFA uses the correlation matrix between observed variables, a factor extraction method and a factor rotation method.
You should place EFA after checking the data and conducting a preliminary reliability analysis, but before creating composite variables for regression. If you are reviewing the broader topic of statistics, you can open the Statistics category to compare EFA with other analysis steps.
Why Exploratory Factor Analysis Matters in Quantitative Research
EFA answers three practical questions. First, are the observed variables related enough for factor analysis? Second, how many factors does the data produce? Third, which factor does each observed variable belong to, and should any variable be removed from the scale?
EFA is often used for a preliminary assessment of the convergent validity and discriminant validity of a scale. Convergent validity means that variables expected to measure the same construct tend to fall on the same factor. Discriminant validity means that groups of variables measuring different constructs are not excessively mixed together.
EFA can also expose problems in your questionnaire. An item may have been translated unclearly, respondents may have understood it differently, or two constructs may be too close in your research context. The Rotated Component Matrix can then show an item loading on several factors or failing to reach the required loading level.
You need to distinguish EFA from simply looking at Cronbach's Alpha. Cronbach's Alpha checks the internal consistency of a group of variables that has already been identified. EFA explores the structure across multiple variables and multiple factors. The two steps complement each other and do not replace each other. The concept of what is a scale is also directly related to identifying observed variables before running EFA.
What Counts as an Acceptable Exploratory Factor Analysis Result
No single number determines whether an EFA is acceptable. You need to read KMO, Bartlett's Test, the number of extracted factors, Total Variance Explained and factor loading together. The thresholds below are commonly used reference points in quantitative research. Your final decision still needs to reflect the theoretical model, sample size and measurement approach.
| Indicator or criterion | Common reference point | Interpretation | Source |
|---|---|---|---|
| KMO | 0.5 or above | The data meet the minimum level of suitability for factor analysis | (Kaiser, 1974) |
| Bartlett's Test of Sphericity | Sig. below 0.05 | The correlation matrix differs from an identity matrix | (Kaiser, 1974) |
| Eigenvalue | Above 1 | The factor is retained under the commonly used rule | (Kaiser, 1960) |
| Total Variance Explained | 50% or above | The retained factors explain a substantial share of the variance | (Hair et al., 2010) |
| Factor loading | 0.5 or above | The observed variable has a sufficient relationship with the factor | (Hair et al., 2010) |
| Corrected Item-Total Correlation | 0.3 or above | The item has an appropriate correlation with the total scale during reliability testing | (Nunnally and Bernstein, 1994) |
A KMO closer to 1 indicates better data suitability, but you should not report KMO while ignoring Bartlett's Test. If Bartlett's Test has Sig. below 0.05, the variables are sufficiently correlated to continue considering EFA. The eigenvalue-above-1 rule is a starting point for identifying the number of factors, not the only evidence of the correct number of factors.
A factor loading of 0.5 or above is commonly treated as acceptable under the benchmark in (Hair et al., 2010). Some older sources use different interpretation bands depending on sample size, so you need to establish one criterion before removing variables. Do not choose the threshold that gives you the most favourable result after seeing the output.
How to Read Exploratory Factor Analysis Output
In SPSS, go to Analyze > Dimension Reduction > Factor. Move the observed variables into the Variables box, select Descriptives and tick KMO and Bartlett's test, select Extraction to view the Scree plot and extraction method, then select Rotation. Varimax is commonly used when the factors are assumed to be independent. If the factors may be correlated, consider an oblique rotation such as Promax instead of applying Varimax automatically.
The first table to inspect is KMO and Bartlett's Test. KMO indicates how suitable the sample is for EFA. The row Bartlett's Test of Sphericity contains the columns Approx. Chi-Square, df and Sig.. Your main focus is KMO and Sig.
Next, review Total Variance Explained. This table contains the columns Total, % of Variance and Cumulative %. The Initial Eigenvalues section shows the initial eigenvalues. Extraction Sums of Squared Loadings and Rotation Sums of Squared Loadings show the variance explained before and after rotation. The retained factors are usually identified from rows with an eigenvalue greater than 1, while also checking the Scree Plot and the theory.
The key table for deciding whether to retain or remove an item is the Rotated Component Matrix. Each row is an observed variable, and each column is a factor. Find the largest factor loading in each row, check whether it reaches the threshold, and then examine the difference between the largest loading and the next largest loading. If an item loads highly on two factors, it has cross-loading and needs to be explained before you decide what to do.
The table below is illustrative output, not the result of a real study. The column names follow the SPSS output format so you know where to look.
| SPSS result | Indicator or variable | Illustrative value | How to read it |
|---|---|---|---|
| KMO and Bartlett's Test | Kaiser-Meyer-Olkin Measure of Sampling Adequacy | 0.812 | Above 0.5, so the data meet the reference level of suitability |
| KMO and Bartlett's Test | Bartlett's Test, Sig. | 0.000 | Statistically significant, so EFA can be considered |
| Total Variance Explained | Component 1, Eigenvalue | 4.286 | Greater than 1, so it is retained under this rule |
| Total Variance Explained | Cumulative % after rotation | 61.438 | Three factors explain 61.438% of the illustrative variance |
| Rotated Component Matrix | TC1 on Component 1 | 0.784 | The factor loading exceeds 0.5 |
| Rotated Component Matrix | TC4 on Component 1 and 2 | 0.536 and 0.512 | Cross-loading is present, so the item needs further review |
With this illustrative output, you cannot conclude that the EFA is acceptable just because KMO is 0.812. Read every row in the Rotated Component Matrix, confirm that each factor contains enough observed variables, and name the factors based on the theoretical content of the variables. Do not name a factor simply because SPSS labels it Component 1 or Component 2.
How to write this in your thesis
Use your own values in the following placeholders: [KMO value], [Bartlett's Test Sig.], [number of factors], [cumulative variance explained], and [factor-loading range]. Report the relevant output tables, explain the retention or removal criteria, and connect the resulting factors to the measurement model.
What to Do When Exploratory Factor Analysis Does Not Meet the Criteria
If KMO is below 0.5, first check the data entry, missing items, reverse coding and variables with zero variance. You should also inspect unusual values and invalid responses. Reviewing outliers may be necessary if some observations are pulling the correlations in an unusual direction, but do not delete data simply to make KMO look better.
If Bartlett's Test does not have Sig. below 0.05, review the group of variables entered into EFA. The variables may belong to concepts that are too different, the sample size may be unsuitable, or the questionnaire may have produced weak correlations. Do not place every independent and dependent variable into one run if the theoretical model requires separate measurement scales.
If an item has a low factor loading, review the item wording and the Communalities table. You can remove the item according to a criterion established in advance, rerun EFA and record each round of processing. EFA rarely produces a completely clean structure on the first run, but every item removal needs both a methodological reason and a content-based reason.
If an item has cross-loading, examine the difference between the two loadings, the item content and the stability of the structure after rerunning the analysis. Removing the item may be reasonable when it does not clearly represent one construct. Combining two factors or renaming a factor simply because the statistical output looks better is usually difficult to defend to your supervisor.
Finally, check the sample size again. A commonly cited rule is approximately 5 to 10 observations for each observed variable (Hair et al., 2010). This is a reference point, not permission to ignore sample quality. If you have run several rounds, save every output file and record which variable was removed, why it was removed and how the results changed.
Distinguishing Exploratory Factor Analysis from Cronbach's Alpha
EFA and Cronbach's Alpha often appear in the scale assessment section, but they answer different questions. EFA examines the grouping structure among many observed variables. Cronbach's Alpha examines whether the variables in an identified group are consistent with one another. Alpha is built from the relationships among variables within the same scale, while EFA examines the full correlation pattern among the variables entered into the analysis.
A scale with a high Alpha can still have an EFA problem. The variables may be highly similar to one another but load on a factor that does not match the theoretical model, or one group may show cross-loading. Conversely, a lower Alpha does not automatically mean that the EFA has failed.
You also need to distinguish EFA from CFA. EFA explores the structure when you do not want to impose the number of factors and the position of each variable completely in advance. CFA tests a measurement structure that has already been specified. If you use SmartPLS, you will usually examine Outer Loadings, CR, AVE and HTMT in the measurement model rather than copying SPSS EFA indicators into the analysis. Concepts such as mediator and moderator belong to the relationship model, not to another name for EFA.
Common Mistakes When Reading EFA
The first mistake is concluding that the EFA is acceptable from KMO alone. KMO may meet the criterion while factor loading, cross-loading or the number of factors remains unsuitable. At a minimum, read the KMO and Bartlett's Test, Total Variance Explained and Rotated Component Matrix tables.
The second mistake is using Sig. = 0.000 to write that the probability is zero. In your thesis, you can write Sig. < 0.001 when SPSS displays 0.000 because of rounding. Also, Bartlett's Sig. does not show that the scale is good. It only shows that the correlation matrix differs sufficiently from an identity matrix to continue considering EFA.
The third mistake is retaining every item with a loading above 0.5 without checking cross-loading. An item loading 0.55 on the first factor and 0.53 on the second factor is less clear than an item loading 0.78 on one factor only. You need to state the loading-difference criterion if your study uses one.
The fourth mistake is forcing the number of factors to match the SPSS output without comparing it with the model. EFA may suggest a structure different from the original hypothesis, but changing the model needs to be explained through the scale content and research foundation. Do not rename factors after every run simply to make them match the results table.
Frequently asked questions
Is Exploratory Factor Analysis the same as exploratory factor analysis?
Yes. Exploratory Factor Analysis is the English name for exploratory factor analysis, commonly abbreviated as EFA. In your thesis, you can write “exploratory factor analysis, Exploratory Factor Analysis, EFA” the first time, then use one form consistently.
What sample size is acceptable for EFA?
There is no single sample size that applies to every dataset. A commonly used benchmark is 5 to 10 observations for each observed variable (Hair et al., 2010), but you also need to examine the number of factors, factor loading, correlation strength and response quality. A large sample does not automatically fix a weak questionnaire or poor-quality data.
Should EFA be run before Cronbach's Alpha?
You will usually check Cronbach's Alpha preliminarily for each scale and then run EFA to examine the overall structure. Some studies may use a different sequence, but you need to explain the reason and keep the method chapter, results chapter and discussion consistent.
Why does EFA produce cross-loading?
Cross-loading occurs when an observed variable has a substantial loading on two or more factors. The wording may not clearly distinguish the two constructs, respondents may interpret the item in several ways, or the two constructs may genuinely be close in your research context. Check the item content, loading difference and theoretical basis before deciding whether to remove it.
Can I run EFA several times until the result is acceptable?
You can rerun EFA after removing an item for a clear reason, but save every round and report the processing criteria. Continually deleting items simply to achieve a better KMO or increase Total Variance Explained makes the result difficult to defend. Check the content meaning, the number of items remaining in each factor and the fit with the original model.
Open your .sav file, make a list of the observed variables, and check KMO, Bartlett's Test, Total Variance Explained and Rotated Component Matrix in sequence instead of looking at one number. If you need to run EFA on real data and turn the output into the interpretation section of your thesis, you can review DoThesis M4 data analysis.