A solution to the ill-posed problem of common factors in vision

Studies investigating individual differences in vision tend to deliver mixed results. Some studies argue for a common factor underlying visual abilities, i.e., a participant performing better in one visual task, compared to another participant, is also assumed to perform better in another visual task. Other studies propose that visual abilities are better explained by several uncorrelated factors, i.e., the performance in one visual task does not necessarily predict performance in another visual task. In the above studies, the data are analyzed with principal component analysis (PCA) or factor analysis (FA). Conclusions are often made based on measures such as the proportion of variance explained by the first component/factor of a PCA/FA. Here, using computer simulations, we demonstrate that we cannot draw conclusions about common factors based on measures such as the proportion of variance explained by the first component/factor of a PCA/FA. Further, we show that the number of participants and variables strongly influence the results of PCA and FA. Finally, we propose a new tool that tests for common factors. We applied our tool to data from 13 previous studies investigating common factors in vision.