# Factor Analysis: A Short Introduction, Part 3-The Difference Between Confirmatory and Exploratory Factor Analysis

by Maike Rahn, PhD

An important question that the consultants at The Analysis Factor are frequently asked is:

What is the difference between a confirmatory and an exploratory factor analysis?

A confirmatory factor analysis assumes that you enter the factor analysis with a firm idea about the number of factors you will encounter, and about which variables will most likely load onto each factor.

Your expectations are usually based on published findings of a factor analysis.

An example is a fatigue scale that has previously been validated. You would like to make sure that the variables in your sample load onto the factors the same way they did in the original research.

In other words, you have very clear expectations about what you will find in your own sample. This means that you know the number of factors that you will encounter and which variables will load onto the factors.

The criteria for variable inclusion are much more stringent in a confirmatory factor analysis than in an exploratory factor analysis. A rule of thumb is that variables that have factor loadings <|0.7| are dropped.

If you would like to include hypothesis testing such as goodness-of-fit tests in your confirmatory factor analysis, you also may want to consider running it in structural equation modeling software, like AMOS, MPlus or LISREL.

An exploratory factor analysis aims at exploring the relationships among the variables and does not have an a priori fixed number of factors. You may have a general idea about what you think you will find, but you have not yet settled on a specific hypothesis.

Or you may have formulated a research question based on your theoretical understanding, and are now testing it.

Of course, in an exploratory factor analysis, the final number of factors is determined by your data and your interpretation of the factors. Cut-offs of factor loadings can be much lower for exploratory factor analyses.

When you are developing scales, you can use an exploratory factor analysis to test a new scale, and then move on to confirmatory factor analysis to validate the factor structure in a new sample.

For example, a depression scale with the underlying concepts of depressed mood, fatigue and exhaustion, and social dysfunction can first be developed with a sample of rural US women using an exploratory factor analysis.

If you would like to next use that scale in a sample of urban US women, you would use a confirmatory factor analysis to validate the depression scale in your new sample.

About the Author: Maike Rahn is a health scientist with a strong background in data analysis.   Maike has a Ph.D. in Nutrition from Cornell University.

#### Go to the next article or see the full series on Easy-to-Confuse Statistical Concepts

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1. Mulugeta says

This is just a simple, yet a perfect explanation of Factor analysis. I wish everything is made as simple as this 🙂

Thank you

Dear Maike,

Great information…
Thank you very much for the clear explanation.
Regards

3. tooba says

can we perform confirmatory factor analysis without performing exploratory factor analysis.
if yes…then what are the conditions???

4. Anwar Ali says

Searched lots for learning EFA and CFA, But the half page intro and example cleared my understanding. Thank you for sharing the valuable information.

5. Jonavan Barnes says

Thank you very much for describing this in a clear and easily understood manner. Because of this, I may now actually finish my PhD!\

Cheers,

Jonavan

6. Krishnamurthy Prabhakar says

Respected Professor,
Thank you very much for your kind clarification. The inputs given by you are simple and comprehensive.
With warm regards
Dr.K.Prabhakar

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