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The special characteristics of items-low reliability, confounds by minor, unwanted covariance, and the likelihood of a general factor-and better understanding of factor analysis means that the default procedure of many statistical packages (Little Jiffy) is no longer adequate for exploratory item factor analysis. It produces too many factors and precludes a general factor even when that means the factors extracted are nonreplicable. More appropriate procedures that reduce these problems are presented, along with how to select the sample, sample size required, and how to select items for scales. Proposed scales can be evaluated by their correlations with the factors; a new procedure for doing so eliminates the biased values produced by correlating them with either total or factor scores. The role of exploratory factor analysis relative to cluster analysis and confirmatory factor analysis is noted.

The purpose of this chapter is to provide a basic but comprehensive treatment of factor analysis. While use of no particular statistical package is assumed, the chapter also provides the information needed to select the options for a factor analysis that are most appropriate to the purpose of a study. The chapter begins with the basic equations and definitions of factor analysis. This section introduces the terms needed to understand factor analytic models and variations in the models. The second section of the chapter presents factor models, including component analysis (CA) and common factor analysis (CFA). Common factor analysis includes both exploratory (ECFA) and confirmatory factor analysis. In addition, all of these variants can be used with correlated or uncorrelated factor models. With each model is presented the essential theoretical information to understand it and the essential practical information to use that model. Each section includes the procedures which now have sufficient empirical and theoretical support to be the generally desired procedures for that model. The concluding section points to elements of all good research designs that need to be remembered in designing a factor analytic study. Included is this section are discussions of the need for high quality variables and how many cases are needed.

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The effects of under-and Overextraction on principal axis factor analysis with varimax rotation were examined in 2 Monte Carlo studies involving 6,420 factor analyses. It was found that (a) when underextraction occurs, the estimated factors are likely to contain considerable error; (b) when Overextraction occurs, the estimated loadings for true factors usually contain substantially less error than in the case of underextraction; and (c) Overextraction can result in factor splitting when a general factor is present and there are no unique variables in the data set. The authors recommend that factor analysts (a) use effective methods to estimate the number of factors; (b) avoid underextraction, even at the risk of Overextraction; and (c) include randomly generated unique variables as "insurance" against factor splitting when a general factor may be present. Researchers conducting exploratory principal axis factor analyses (PFA) seldom know beforehand how many factors underlie their data. This uncertainty creates a practical dilemma: How many factors should be extracted if the true number of factors is unknown? The decision is especially difficult because little is known regarding the effects of underextraction (extracting too few factors) and Overextraction (extracting too many) on the quality of the factor analytic solution.Researchers have dealt with this dilemma in a variety of ways. Many have relied on Kaiser's (1960) eigenvalues-greater-than-1 rule to determine the number of factors. Although several studies have indicated that this rule is unsatisfactory (Hakstian, Rogers, &