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Factor Analysis: Confirmatory & Exploratory

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  • 0:04 Factor Analysis Introduction
  • 0:49 What Is a Factor Analysis?
  • 2:14 Exploratory Factor Analysis
  • 3:10 Confirmatory Factor Analysis
  • 4:05 Lesson Summary
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Lesson Transcript
Instructor: Yolanda Williams

Yolanda has taught college Psychology and Ethics, and has a doctorate of philosophy in counselor education and supervision.

A factor analysis is a statistical procedure that is used in order to find underlying groups of related factors in a set of observable variables. Learn about the different types of factor analyses and more.

Factor Analysis Introduction

Suppose you were researching grades of college freshmen in an honor's Liberal Arts program. Your study sample consists of 150 college freshmen, all who have taken five end-of-the-year exams. One exam covers mathematics, one covers English literature, one covers science, and the other two cover Latin and writing.

The students' grades on each of the five exams are positively correlated with each other: this means that students who have high grades on one exam usually have high grades on the others. However, you find that there are some students who are only good at two or three subjects. You start to wonder if the students' performances on the five exams could be determined by different types of intellectual abilities. One way to answer this question is by conducting a factor analysis.

What Is a Factor Analysis?

Factor analysis is a statistical method that is used to investigate whether there are underlying latent variables, or factors, that can explain the patterned correlations within a set of observed variables. In this case, the observed variables would be the five exam scores. Latent variables are underlying constructs that are not directly observable and cannot be measured by one single thing. For example, you cannot directly measure the quality of someone's marriage. Instead, you can use a combination of observable variables to measure marriage quality, including the amount of time the couple spends together, the environment, marital conflict, marital attitudes, etc.

The primary goals of factor analysis are as follows:

  1. Determine how many factors underlie a set of observable variables
  2. Provide a method of explaining variance among observable variables by using fewer, newly created factors
  3. Reduce data by allowing the user to extract a small set of factors (which usually are not related to each other) from a larger set of observable variables (which are usually correlated with each other). This allows for summarization of a large number of variables into a smaller number of factors
  4. Define the meaning or content of the factors

There are two types of factor analyses: exploratory factor analysis (or EFA) and confirmatory factor analysis (or CFA).

Exploratory Factor Analysis

EFA is used in situations when you do not have a predetermined idea of how many factors there are or the relationship between the factors and the observed variables. The purpose of the EFA is to explore the structure of the factors. The goal is to find the underlying relationships that exist between the variables.

Suppose that you decided to take the data that you collected from the 150 college freshman and conduct an EFA. You're not sure if there are any underlying relationships between the variables, and you have no hypothesis as to what the relationships might be. You are just curious to see if you can find any underlying factors.

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