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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.

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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.You run the exploratory factor analysis and find that there are two factors. Students who have high scores in math and science are high on the first factor, while students who have high scores on English, Latin, and writing are high on the second factor. You have just figured out the underlying factor structure using EFA.

Confirmatory Factor Analysis

CFA is used in situations where you have a specific hypothesis regarding how many factors there are and which observed variables are related to each factor.

The hypothesis is usually based on previous research or theory. The purpose of CFA is to confirm that there is a relationship between the factors and the observed variables.Suppose in the example above, you notice that some students are good at math and science and have lower scores on English literature, Latin, and writing. There are also students who scored high on English literature, Latin, and writing but did not do so well on math and science.You may hypothesize that the students’ performances on the five exams could be determined by the two types of intellectual abilities. Specifically, math and science are determined by one type of intellectual ability, while English literature, Latin, and writing performance are determined by another type of intellectual ability.

In this example, you would perform a CFA.

Lesson Summary

Factor analysis is a statistical method that is used to determine whether a group of observable variables are related to a smaller group of underlying factors. CFA and EFA are the two types of factor analysis. There are differences between CFA and EFA.CFA requires you to predetermine a specific hypothesis based on previous research or theory, the number of factors, and which observable variables are related to each factor.

EFA does not require you to predetermine the number of factors or the relationship between the factors and the observed variables. EFA identifies the factor structure and can explain a maximum variance amount.

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