Understanding and Using Factor Scores: …

1 A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to the practical Assessment, Research & Evaluation. Permission is granted to distribute this article for nonprofit, educational purposes if it is copied in its entirety and the journal is credited. Volume 14, Number 20, October 2009 ISSN 1531-7714. Understanding and Using Factor Scores: Considerations for the Applied Researcher Christine DiStefano Min Zhu Diana M ndril . University of South Carolina Following an exploratory Factor analysis, Factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual's placement on the Factor (s). This article discusses popular methods to create Factor scores under two different classes: refined and non-refined.

2 Strengths and considerations of the various methods, and for Using Factor scores in general, are discussed. Exploratory Factor analysis (EFA) has been used as an identified from the EFA. These Factor scores1 may then be analytical tool in educational research. The methods used to investigate the research questions of interest. may be used with novel or exploratory research This article will describe ways in which a researcher scenarios as a precursor to latent variable modeling or may create Factor scores following an EFA and will confirmatory Factor analyses (CFA) (Schumaker &. discuss the advantages and disadvantages among the Lomax, 2004). However, in many research situations, methods. There are two primary classes of computing EFA is used as the focal methodology. Practitioners Factor scores: refined methods to develop Factor scores may use EFA for a variety of purposes such as reducing require technical analyses, while non-refined methods a large number of items from a questionnaire or survey involve non-sophisticated procedures.

3 In this article, we instrument to a smaller number of components, discuss issues related to computing Factor scores so uncovering latent dimensions underlying a data set, or practitioners may make informed decisions when examining which items have the strongest association choosing among methods. with a given Factor . Once a researcher has used EFA and has identified the number of factors or components Using and Computing Factor Scores underlying a data set, he/she may wish to use the information about the factors in subsequent analyses Creation and use of Factor scores is an option in EFA. (Gorsuch, 1983). For example, researchers may want to and with covariance structural modeling ( , CFA, identify an individual's placement or ranking on the structural equation modeling) situations.

4 The distinction Factor (s), use the information with hypothesis tests to of which methodology to use (EFA, CFA, structural determine how Factor scores differ between groups, or to incorporate Factor information as part of a regression 1 We recognize that the EFA literature makes a distinction between or predictive analysis. To use EFA information in Factor scores and Factor score estimates, where Factor scores follow-up studies, the researcher must create scores to generally refer to situations where the generated Factor scores are unique and Factor score estimates relate to solutions where there represent each individual's placement on the Factor (s) can be more than one possible solution for the Factor score. To simplify the discussion, this article will refer to Factor scores meaning all types of scores indicating relative placement on an identified Factor following an EFA.)

5 practical Assessment, Research & Evaluation, Vol 14, No 20 Page 2. DiStefano, Zhu & M ndril , Computing Factor Scores models) depends on many issues, such as the goal of the For example, many Factor score methods are built on the project, the nature of the work ( , exploratory or assumption that the resulting Factor scores will be confirmatory research), and even issues such as uncorrelated; however, orthogonal factors are often the researchers' knowledge of methodology, statistical rarity rather than the norm in educational research. techniques, and software. While latent variable modeling Increased knowledge of the requirements underlying procedures are very popular, use of Factor scores in the many of the Factor score methods may provide EFA framework is taught in graduate courses in research assistance to researchers interested in Using these methods, included in many multivariate textbooks ( , techniques.

6 Hair, Black, Babin, Anderson, & Tatham, 2006) and There are two main classes of Factor score used in educational research situations. computation methods: refined and non-refined. To examine situations where Factor scores were Non-refined methods are relatively simple, cumulative used, a brief literature review of peer reviewed articles procedures to provide information about individuals'. from the social sciences was conducted Using the placement on the Factor distribution. The simplicity PSYCINFO database. The key words Factor analysis lends itself to some attractive features, that is, and Factor scores were used to identify articles. We non-refined methods are both easy to compute and easy examined recent articles published between the years to interpret. Refined computation methods create Factor 2000 - 2009, inclusive.

7 The search uncovered a total of scores Using more sophisticated and technical 229 application articles that created and used Factor approaches. They are more exact and complex than scores in subsequent analyses. The articles spanned a non-refined methods and provide estimates that are variety of disciplines including education, psychology, standardized scores. public health and law. Factor scores were used for Non-refined Methods various purposes in the field of educational research. For example, Kawashima and Shiomi (2007) used EFA with Non-refined methods are simple to use. Under the class a thinking disposition scale. The analyses uncovered of non-refined methods, various methods exist to four factors related to high school students' attitudes produce Factor scores.

8 The most frequently used towards critical thinking. Using students' Factor scores, methods are described below. Analysis of Variance was conducted by Factor to 1. Sum Scores by Factor investigate student differences in attitude by grade level and gender. Similarly, EFA was adopted by Bell, One of the simplest ways to estimate Factor scores for McCallum, and Cox (2003) in their research of cognitive each individual involves summing raw scores elements underlying reading. After the Factor solution corresponding to all items loading on a Factor (Comrey was determined, Factor scores were calculated for each & Lee, 1992). If an item yields a negative Factor loading, Factor , and were used in the follow-up multiple the raw score of the item is subtracted rather than added regression analyses to investigate the capability of the in the computations because the item is negatively factors in predicting selected reading and writing skills.

9 Related to the Factor . For this method (as well as for the While articles which used Factor scores with EFA following non-refined methods) average scores could be and also confirmatory Factor analysis CFA procedures computed to retain the scale metric, which may allow for were noted in our brief literature review, the majority of easier interpretation. Also, average scores may be useful these articles (123 or ) used Factor scores to foster comparisons across factors when there are following EFA rather than CFA procedures 2 . differing numbers of items per Factor . Additionally, many studies Using Factor scores did not The sum score method may be most desirable when clarify the computation procedure used to create the the scales used to collect the original data are untested Factor scores.

10 And exploratory, with little or no evidence of reliability or Although Factor scores following EFA are still in validity (Hair et al, 2006, p. 140). In addition, summed use, the practice has been controversial in the social Factor scores preserve the variation in the original data. sciences for many years ( , Glass & Maguire, 1966). Tabeachinck and Fidell (2001) noted that this approach is generally acceptable for most exploratory research 2 Of the 229 application articles Using Factor scores: 123 articles situations. ( ) used EFA, 43 articles ( ) used latent variable modeling or confirmatory Factor analysis procedures, and 63 articles ( ). While sum scores may be acceptable for many did not provide sufficient information on the methodology used. studies, there are some considerations.