Unfortunately, much of the literature that has attempted to address sample size guidelines for EFA, particularly the studies attempting to dismiss subject to item ratios, use flawed data. We will purposely not cite studies here to protect the guilty, but consider it sufficient to say that many of these studies either tend to use highly restricted ranges of subject to item ratios or fail to adequately control for or vary other confounding variables (e.g., factor loadings, number of items per scale or per factor/component) or restricted range of N. Some of these studies purporting to address subject to item ratio fail to actually test subject to item ratios in their analyses.

Researchers seeking guidance concerning sufficient sample size in EFA are left between two entrenched camps—those arguing for looking at total sample size and those looking at ratios.[1] This is unfortunate, because both probably matter in some sense, and ignoring either one can have the same result: errors of inference. Failure to have a representative sample of sufficient size results in unstable loadings (Cliff, 1970), random, nonreplicable factors (Aleamoni, 1976; Humphreys, Ilgen, McGrath, & Montanelli, 1969), and lack of generalizability to the population (MacCallum, Widaman, Zhang, & Hong, 1999).

If one were to take either set of guidelines (e.g., 10:1 ratio or a minimum N of 400 to 500) as reasonable guidelines, a casual perusal of the published literature shows that a large portion of published studies come up short. One can easily find articles reporting results from EFA or PCA based on samples with fewer subjects than items or parameters estimated that nevertheless draw substantive conclusions based on these questionable analyses. Many more have hopelessly insufficient samples by either guideline.

One survey by Ford, MacCallum, and Tait (1986) examined common practice in factor analysis in industrial and organizational psychology during the ten-year period of 1974 to 1984. They found that out of 152 studies using EFA or PCA, 27.3% had a subject to item ratio of less than 5:1 and 56% had a ratio of less than 10:1. This matches the perception that readers of social science journals get, which is that often samples are too small for the analyses to be stable or generalizable.

Osborne and colleagues published the results of a survey of current practices in the social sciences literature (Osborne, Costello, & Kellow, 2008). In this survey, they sampled from two years’ (2002, 2003) worth of articles archived in PsycINFO that reported some form of EFA and listed both the number of subjects and the number of items analyzed (303 total articles surveyed). They standardized their sample size data via a subject to item ratio. The results of this survey are summarized in Current practice in factor analysis in 2002-2003 psychology journals. A large percentage of researchers report factor analyses using relatively small samples. In a majority of the studies (62.9%) researchers performed analyses with subject to item ratios of 10:1 or less. A surprisingly high proportion (almost one-sixth) reported factor analyses based on subject to item ratios of only 2:1 or less (note that in this case there would be more parameters estimated than subjects if more than one factor is extracted).

A more recent survey of EFA practices in four psychological journals, Educational and Psychological Measurement, Journal of Educational Psychology, Personality and Individual Differences, and Psychological Assessment, identifies similar trends. Among the 60 studies reviewed, Henson and Roberts’ (2006) found a median sample size of 267 for reported EFAs, a mean subject to item ratio of 11, and a median of 60 parameters (20 items x 3 factors) estimated. As you will see below, these are not comforting statistics. Given the stakes and the empirical evidence on the consequences of insufficient sample size, this is not exactly a desirable state of affairs.