• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • Our Programs
    • Membership
    • Online Workshops
    • Free Webinars
    • Consulting Services
  • About
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Collaborate with Us
  • Statistical Resources
  • Contact
  • Blog
  • Login

How Big of a Sample Size do you need for Factor Analysis?

by Karen Grace-Martin 2 Comments

Most of the time when we plan a sample size for a data set, it’s based on obtaining reasonable statistical power for a key analysis of that data set. These power calculations figure out how big a sample you need so that a certain width of a confidence interval or p-value will coincide with a scientifically meaningful effect size.

But that’s not the only issue in sample size, and not every statistical analysis uses p-values.

One example is Factor Analysis.*

A factor analysis is a measurement model of an underlying construct. So like regression models, structural equation models, and latent class models, the focus in on understanding the structure of the relationships among variables.

factor_analysisThe specific focus in factor analysis is understanding which variables are associated with which latent constructs. The approach is slightly different if you’re running an exploratory or a confirmatory model, but this overall focus is the same.

If power isn’t the main issue, how big of a sample do you need in factor analysis?

The short answer is: a big one.

The long answer is a little more complicated, mainly because there isn’t one right answer. Authors have differing opinions on exactly how many subjects you need, and on exactly which criterion to use.

Sample Size Rules of Thumb

For example, some authors use a criterion based on the total sample size:

— 100 subjects=sufficient if clear structure; more is better (Kline, 1994)
— 100 subjects=poor; 300 =good; 1000+ = excellent (Comrey & Lee, 1992)
— 300 subjects, though fewer works if correlations are high among variables (Tabachnik & Fidell, 2001)

Others base it on a ratio of the number of cases to the number of variables involved in the factor analysis:

— 10-15 subjects per variable (Pett, Lackey, & Sullivan)
— 10 subjects per variable (Nunnally, 1978)
— 5 subjects per variable or 100 subjects, whichever is larger (Hatcher, 1994)
— 2 subjects per variable (Kline, 1994)

And then others base it on a ratio of cases to the number of factors:
20 subjects per factor (Arrindel & van der Ende, 1985).

Rules of Thumb are not Rules

But the reality is these are rules of thumb, not rules. More recent simulation studies have found that the required sample size depends on a number of issues in the data and in the model, working together. They include all the issues listed above and a few more.

Here are a few takeaways:

1. You’re going to need a large sample. That means in the hundreds of cases. More is better.

2. You can get away with fewer observations if the data are well-behaved. If there are no missing data and each variable highly loads on a single factor and not others, you won’t need as many cases. But counting on the data behaving is like counting on the weather behaving during hurricane season. You’ll have a better outcome most of the time if you plan for the worst.

3. The main issue with small data sets is overfitting (a secondary issue is if the sample is really small, the model won’t even converge). It’s a simple concept: when a sample is too small, you can get what looks like good results, but you can’t replicate those results in another sample from the same population.

All the parameter estimates are so customized to this particular sample, that they’re not useful for any other sample. This can, and does, happen in any model, not just factor analysis.

*Yes, Confirmatory Factor Analysis can use p-values, for overall model fit chi-square tests as well as specific path coefficients. Exploratory Factor Analysis does not.

Wolf, E., K. Harrington S. Clark, and M. Miller (2013). Sample Size Requirements for Structural Equation Models: An Evaluation of Power, Bias, and Solution Propriety, Educ Psychol Meas. 2013 December ; 76(6): 913–934.

Costello, A. and Osborne, J. (2005). Exploratory Factor Analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research, and Evaluation, 10(7), 1-9.

 

Principal Component Analysis
Summarize common variation in many variables... into just a few. Learn the 5 steps to conduct a Principal Component Analysis and the ways it differs from Factor Analysis.

Tagged With: Factor Analysis, p-value, rules of thumb, sample size

Related Posts

  • Member Training: Matrix Algebra for Data Analysts: A Primer
  • Measurement Invariance and Multiple Group Analysis
  • Why Adding Values on a Scale Can Lead to Measurement Error
  • One of the Many Advantages to Running Confirmatory Factor Analysis with a Structural Equation Model

Reader Interactions

Comments

  1. Edwin says

    January 17, 2022 at 2:55 pm

    Thank you for the information. It is useful for my dissertation.

    Reply
  2. Tesfaye says

    June 22, 2021 at 7:21 am

    Helpful resources for a Ph.D. student indeed! Thank you!

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Please note that, due to the large number of comments submitted, any questions on problems related to a personal study/project will not be answered. We suggest joining Statistically Speaking, where you have access to a private forum and more resources 24/7.

Primary Sidebar

This Month’s Statistically Speaking Live Training

  • Member Training: Analyzing Pre-Post Data

Upcoming Free Webinars

Poisson and Negative Binomial Regression Models for Count Data

Upcoming Workshops

  • Analyzing Count Data: Poisson, Negative Binomial, and Other Essential Models (Jul 2022)
  • Introduction to Generalized Linear Mixed Models (Jul 2022)

Copyright © 2008–2022 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Non-necessary
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.
SAVE & ACCEPT