EFA vs CFA: When to Use Each and How to Report Factor Analysis

What Is Factor Analysis, in Plain English?

Imagine you give students a 20-item questionnaire about study motivation. Some items ask about enjoying learning, others about feeling confident before exams, and others about worrying over grades. When you look at the answers, you notice a pattern: students who agree with one enjoyment item tend to agree with the others too. The same happens with the confidence items and the worry items. Factor analysis is the statistical technique that finds these hidden groupings, called factors, behind your observed items.

In other words, factor analysis asks whether a smaller number of underlying dimensions can explain the correlations among many measured variables. If yes, twenty items can be summarised with three or four meaningful factors.

There are two main types, and choosing the wrong one is a common thesis mistake. Exploratory factor analysis (EFA) is used when you are discovering the structure. Confirmatory factor analysis (CFA) is used when you already have a theory about the structure and want to test it. This post explains both, shows you when to use each, and walks you through how to report them.

What Is Exploratory Factor Analysis (EFA)?

Exploratory factor analysis is a data-driven technique. You do not tell the analysis in advance how many factors there should be or which items belong to which factor. Instead, you let the pattern of correlations in your data suggest the structure. EFA is the right choice when you are developing a new questionnaire, adapting a scale to a new population, or exploring a construct that has not been clearly mapped out before.

The typical EFA workflow looks like this:

1. Check that your data are suitable. Look at the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy and Bartlett’s test of sphericity. A KMO value above .60 is generally considered acceptable, and a significant Bartlett’s test suggests your variables are correlated enough for factor analysis to be worthwhile.
2. Decide how many factors to keep. Common approaches include eigenvalues greater than 1, the scree plot elbow, and parallel analysis. Do not rely on a single rule; use several together and let theory guide the final decision.
3. Extract and rotate the factors. Rotation, such as varimax or promax, makes the factor pattern clearer and easier to interpret. An oblique rotation like promax is often more realistic in the social sciences, because factors such as anxiety and depression are usually correlated with each other.
4. Interpret the factor loadings. A loading shows how strongly an item relates to a factor. Loadings above .40 are often treated as meaningful, items that load strongly on more than one factor (cross-loadings) need a closer look, and items with no strong loading may need to be dropped or rewritten.
5. Name the factors and check reliability. Give each factor a clear, defensible name based on its items, then check the internal consistency of each factor, for example with Cronbach’s alpha.

EFA answers the question: “What structure is hiding in my data?”

What Is Confirmatory Factor Analysis (CFA)?

Confirmatory factor analysis works the other way round. You begin with a specific model, usually based on theory or previous research, and you test whether your data fit that model. You specify in advance how many factors there are, which items load on which factor, and whether the factors are allowed to correlate. The analysis then tells you how well that model matches your data.

A CFA workflow typically involves:

1. Specify the model from theory. Draw or write out the expected structure before you look at the results. For example, a wellbeing scale might be hypothesised to have three factors: positive emotion, engagement, and relationships, each measured by four items.
2. Estimate the model. CFA is usually run as a form of structural equation modelling, using software such as AMOS, lavaan in R, or Mplus.
3. Judge model fit. No single number tells the whole story, so researchers report several fit indices together. Commonly reported indices include the chi-square test, the Comparative Fit Index (CFI), the Tucker-Lewis Index (TLI), the Root Mean Square Error of Approximation (RMSEA), and the Standardized Root Mean Square Residual (SRMR). As a rough guide, CFI and TLI values of .95 or above, RMSEA of .06 or below, and SRMR of .08 or below are often described as indicating good fit, but always interpret them alongside your sample size, model complexity, and theory.
4. Inspect the loadings and modification indices. Check that items load sensibly on their intended factors. Modification indices suggest changes that would improve fit, but you should only make a change if it makes theoretical sense, never just to chase a better number.
5. Report the model clearly. State the hypothesised structure, the fit indices, the standardised loadings, and whether the model was accepted, revised, or rejected.

CFA answers the question: “Does my data support the structure I predicted?”

EFA vs CFA: The Key Differences at a Glance

When to Use EFA and When to Use CFA

Use this decision guide:

1. Are you building something new? If you wrote a new set of items and have no established theory about their structure, start with EFA.
2. Are you testing something established? If a scale already has a published factor structure and you want to check whether it holds in your sample, use CFA.
3. Are you adapting a scale? If you translated a scale or used it with a very different population, EFA first is usually wise. If the EFA supports the original structure, a CFA on a fresh sample is the stronger follow-up.
4. Do you have one sample or two? The strongest design is to run EFA on one half of your sample and CFA on the other half. Running both on the same data and treating the CFA as independent confirmation is a mistake, because the model was built from the very data used to test it.
5. What does your supervisor or journal expect? Scale development papers usually report EFA, sometimes followed by CFA. Validation papers usually report CFA, and reviewers will expect fit indices, not just loadings.

Rule of thumb: explore first, confirm second.

A Worked Example: From EFA to CFA

Suppose a student, Ayesha, designs a 12-item questionnaire to measure “academic confidence” among undergraduates. She has no published model to follow, so she begins with EFA. Her KMO is .82 and Bartlett’s test is significant. The scree plot and parallel analysis both point to two factors: six items about believing in one’s ability, and six about staying calm under exam pressure. She names them “self-belief” and “composure under pressure”.

A year later, another student uses the questionnaire with postgraduates. The structure is now hypothesised, so CFA is the right analysis. She specifies the two-factor model and reports the fit indices. Good fit supports the structure in the new sample; poor fit calls for theoretically justified revision, not deleting items until the numbers look nice.

Notice the sequence: the same questionnaire needed EFA when its structure was unknown and CFA once its structure was proposed. The question you are asking, not the questionnaire itself, decides the method.

How to Report EFA Results

A clear EFA report includes: the sample size and suitability checks (KMO and Bartlett’s test), the extraction and rotation methods, how you decided the number of factors, the percentage of variance explained, a factor loading table with cross-loadings shown, items dropped and why, and the reliability of each factor. In APA style, report the key statistics in text and put the full loading matrix in a table, so readers can judge your decisions for themselves.

Example sentence: “An exploratory factor analysis using principal axis factoring with promax rotation was conducted on the 12 items. The Kaiser-Meyer-Olkin measure was .82 and Bartlett’s test of sphericity was significant, indicating the data were suitable for factor analysis. Two factors with eigenvalues greater than 1 were retained, together explaining 58% of the variance.”

How to Report CFA Results

A clear CFA report includes: the hypothesised model described before the results, the estimation method, the full set of fit indices with their values (not just the ones that look good), the standardised factor loadings, any theoretically justified modifications, and a conclusion about whether the model was supported. Always report fit indices even when the fit is poor; hiding a bad fit is a serious reporting problem.

Example sentence: “A confirmatory factor analysis tested the hypothesised two-factor model. The model showed acceptable fit to the data, CFI = .96, TLI = .95, RMSEA = .05, SRMR = .06. All items loaded significantly on their intended factors, with standardised loadings ranging from .58 to .84.”

Common Mistakes to Avoid

• Running CFA with no theory. If you have no hypothesised structure, CFA is the wrong tool. Explore first.
• Running EFA and CFA on the same sample and calling it validation. Split your sample or collect fresh data for the confirmatory step.
• Judging fit by one index. Chi-square is sensitive to sample size, so report CFI, TLI, RMSEA, and SRMR together.
• Deleting items purely to improve fit. Every change should make theoretical sense, and all changes should be reported transparently.
• Keeping every factor the software suggests. A factor with only one or two items, or with no sensible interpretation, is usually not a real factor.
• Forgetting reliability. A neat factor structure means little if the factors are not measured reliably. Report reliability for each factor.
• Using a tiny sample. Factor analysis with 40 participants rarely gives stable results. Plan your sample size before data collection, not after.

Frequently Asked Questions

Is EFA easier than CFA?

EFA is simpler to run in SPSS, but it is not necessarily easier to do well. Deciding how many factors to keep and interpreting cross-loadings takes judgement. CFA requires more statistical background, but its rules about model fit are more standardised. Neither is a shortcut.

Do I need CFA if my EFA looks clean?

Not always. For a coursework project or a thesis chapter, a well-reported EFA is often enough. CFA becomes important when you are publishing a new scale, validating an existing one, or making claims that depend on the structure holding up in new samples.

What sample size do I need for factor analysis?

Common guidance is at least 100 participants for EFA and at least 200 for CFA, with larger samples giving more stable results. Very small samples produce factor solutions that rarely replicate.

What should I do if my CFA model does not fit?

First, check for data problems such as misunderstood or incorrectly reverse-scored items. Then inspect loadings and residuals, and only then consider theoretically justified modifications, reporting every change. If the model still does not fit, that is a finding: the proposed structure does not describe your data.

Can I use SPSS for CFA?

SPSS Statistics on its own does not run CFA; you need SPSS Amos, or a package such as lavaan in R or Mplus. EFA, by contrast, is available directly in SPSS Statistics, which is one reason students often start there.

Final Takeaway

EFA and CFA are partners, not rivals. EFA helps you discover the structure hiding in your data when you do not yet know what it is. CFA helps you test a structure you have already proposed, so you can say with evidence whether it holds. Choose based on your research question, report your decisions transparently, and never let a good-looking fit index substitute for a theoretically sensible model.