Testing bipolarity.

Many psychological dimensions seem bipolar (e.g., happy-sad, optimism-pessimism, and introversion-extraversion). However, seeming opposites frequently do not act the way researchers predict real opposites would: having correlations near -1, loading on the same factor, and having relations with external variables that are equal in magnitude and opposite in sign. We argue these predictions are often incorrect because the bipolar model has been misspecified or specified too narrowly. We therefore explicitly define a general bipolar model for ideal error-free data and then extend this model to empirical data influenced by random and systematic measurement error. Our model shows the predictions above are correct only under restrictive circumstances that are unlikely to apply in practice. Moreover, if a bipolar dimension is divided into two so that researchers can test bipolarity, our model shows that the correlation between the two can be far from -1; thus, strategies based upon Pearson product-moment correlations and their factor analyses do not test if variables are opposites. Moreover, the two parts need not be mutually exclusive; thus, measures of co-occurrence do not test if variables are opposites. We offer alternative strategies for testing if variables are opposites, strategies based upon censored data analysis. Our model and findings have implications not just for testing bipolarity, but also for associated theory and measurement, and they expose potential artifacts in correlational and dimensional analyses involving any type of negative relations. (PsycInfo Database Record (c) 2024 APA, all rights reserved).