The Effect of Common Variance and Structure Pattern on Random Data Eigenvalues: Implications for the Accuracy of Parallel Analysis

Abstract

Selecting the correct number of factors to retain in a factor analysis is a crucial step in developing psychometric tools or developing theories. The present study assessed the accuracy of parallel analysis, a technique in which the observed eigenvalues are compared to eigenvalues from simulated data in which no real factors are present. Study 1 investigated the effect of the presence of one real factor on the size of subsequent noise eigenvalues. The size of real factors and the sample size were manipulated. Study 2 examined the effect that the pattern of structure coefficients and continuousness of the variables have on the size of real and noise eigenvalues. Study 3 compared the results of Studies 1 and 2 to actual psychometric data. These examples illustrate the importance of modeling the data more closely when parallel analysis is used to determine the number of real factors.