This document discusses exploratory factor analysis (EFA), including its concepts, theory, and process. EFA is commonly used to reduce a large number of variables into a smaller set of underlying factors and establish relationships between measured variables and latent constructs. The key steps of EFA include assessing suitability of the data, extracting factors, determining the number of factors to retain, rotating the factors for better interpretation, and labeling the factors. Sample size, factor extraction and rotation methods, and interpretation are also covered.

1. Exploratory Factor Analysis;
Concepts and Theory
Dr. Hamed Taherdoost
Founder of Hamta Group
OBS Tech Limited
Hamta Academy
Senior Member of IEEE
(www.hamta.org)

2. HELLO!I AM HAMED TAHERDOOST,
the award-winning leader and R&D Professional, and the founder of
Hamta Group.
I have over two decades of experience in both industry and academic
sectors, and I have been highly involved in development of several
important projects in different industries .
I have been an active multidisciplinary researcher working with
researchers from various disciplines and have been actively engaged in
several academic and industrial research projects.
My views on science and technology have been published in top-ranked
scientific publishers such as Elsevier, Springer, Emerald, IEEE, IGI Global,
Inderscience, Taylor and Francis and have published over 120 scientific
articles, seven book chapters as well as six books in the field of
technology and research methodology.
I am Senior Member of IEEE, IASED, IEDRC, Working group member of
IFIP TC 11, Member of CSIAC, & ACT-IAC. 2

3. Factor Analysis
 Factor analysis (FA) has origins dating back 100 years through the work of
Pearson and Spearman (Spearman 1904). Factor analysis as a multivariate
statistical procedure, is commonly utilized in the fields of information system,
psychology, commerce and education and is considered the approach of
choice for interpreting self-reporting survey (Byrant, Yarnold et al. 1999).
 FA reduces a large number of variables (factors) into a smaller set.
Furthermore, it establishes underlying dimensions between measured factors
and latent constructs, thereby allowing the formation and refinement of
theory. Moreover, it provides construct validity evidence of self-reporting
scales (Hair, et al. 1995; Tabachnick and Fidell 2001; Thompson 2004) .
 Factor analysis is divided to two main categories namely; Exploratory Factor
Analysis (EFA), and Confirmatory Factor Analysis (CFA)
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4. Exploratory Factor Analyses
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Despite exploratory factor analysis being a apparently complex statistical method,
the approach taken in the analysis is sequential and linear, involving many options
(Thompson 2004). Objectives of Exploratory Factor Analysis (Pett, et al. 2003) are:
 Reduction of number of factors (variables)
 Assessment of multicollinearity among factors which are correlated
 Unidimensionality of constructs evaluation and detection
 Evaluation of construct validity in a survey
 Examination of factors (variables) relationship or structure
 Development of theoretical constructs
 Prove proposed theories

5. Steps toward Implementing EFA
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Evaluation of Data Suitability for EFA
Factor Extraction Method
Factor Retention Method
Selection of Rotational Method
Interpretation and Labeling

6. Sample Size
 Sample size is a significant issue FA
 Hair, et al. (1995a) suggested that sample sizes should be 100 or greater
 Comrey (1973) stated in his guide to sample sizes: 100 as poor, 200 as fair, 300
as good, 500 as very good, and 1000 or more as excellent
 The stronger the data, the smaller the sample can be for an accurate analysis.
“Strong data” in factor analysis means uniformly high communalities without
cross loadings, plus several variables loading strongly on each factor
 A larger sample can help determine whether or not the factor structure and
individual items are valid
 Sampling adequacy provides the researcher with information regarding the
grouping of survey items
 The sampling adequacy can be assessed by examining the Kaiser-Meyer-Olkin
(KMO)
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7. Factor Extraction
 There are several ways to extract factors:
 Principal Components Analysis (PCA)
 Principal Axis Factoring (PAF)
 Image Factoring
 Maximum Likelihood
 Alpha Factoring
 Unweighted Least Squares
 Generalised Least Squares
 Canonical
 However, principal components analysis, maximum likelihood and principal
axis factoring are used most commonly . 7

8. Factor Retention Methods
 After extraction phase, the researcher must decide how many constructs to
retain for rotation. Factor retention is more important than other phases.
 Factor retentions methods are;
 Cumulative percent of variance extracted
 Kaiser‟s criteria (eigenvalue > 1 rule)
 Scree test
 Parallel Analysis
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9. Selection of Rotational Method
 In order to produce a more interpretable and simplified solution, rotation will
help by maximizing high item loadings and minimizing low item loadings.
Oblique and orthogonal rotations are two types of rotation technique.
 Oblique rotation is more accurate while data does not meet priori
assumptions .
 Orthogonal rotation produces factors that are uncorrelated. Orthogonal
method has several options for rotation; quartimax, varimax, and equamax..
 Varimax rotation which was developed by (Thompson 2004) is the most
common form of rotational methods for exploratory factor analysis and will
often provide a simple structure.
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10. Interpretation
 Interpretation is the process of examination to select variables which are
attributable to a construct and allocating a name for that construct.
 The labeling of constructs is a theoretical, subjective and inductive process.
 It is significant that labels of constructs reflect the theoretical and conceptual
intent.
 For instance, a construct may includes four variables which all related to the
user satisfaction thus the label “user satisfaction” will be assigned for that
construct.
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11. THANKS!
ANY QUESTIONS?
You can find me at:
in/hamed.taherdoost
RG.net/hamed.taherdoost
orcid.org/0000-0002-6503-6739
hamed@hamta.org
hamed.taherdoost@gmail.com
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12. “Hamed Taherdoost, 2014, Exploratory Factor Analysis; Concepts and Theory, Advances in
Applied and Pure Mathematics, Page: 375-382.
Hamed Taherdoost, 2017, Determining Sample Size; How to Calculate Survey Sample Size,
International Journal of Economics and Management Systems, Volume 2, Page: 237-239.
Tabachnick and Fidell, 2001, Using multivariate statistics. MA, Allyn & Bacon.
Hair, Anderson, et al., 1995, Multivariate data analysis. New Jersey, Prentice-Hall Inc.
Thompson, 2004, Exploratory and confirmatory factor analysis: understanding concepts and
applications. Washington, DC, American Psychological Association.
Pett, Lackey, et al., 2003, Making Sense of Factor Analysis: The use of factor analysis for
instrument development in health care research. California, Sage Publications Inc.
Hamed Taherdoost, H. 2016. How to Design and Create an Effective Survey/Questionnaire; A
Step by Step Guide. International Journal of Advance Research in Management, 5(4), 37-41.
Hamed Taherdoost, 2016, Validity and Reliability of the Research Instrument; How to Test
the Validation of a Questionnaire/Survey in a Research, International Journal of Academic
Research in Management, Volume. 5, No. 3, Page: 28-36.
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