The actual capacity to perform tasks, and actual fatigue, are concepts that have been thought of as inherently linked. These considerations also extend to their phenomenology, meaning the perception(s) of capacity or fatigue. The phenomenology of capacity or fatigue thus may be capturing the same underlying latent construct. Further, it is speculated that the actual capacity of a person to perform a given task, and their perception of that capacity, have a psychophysical relationship. The aim of this study was therefore twofold: 1) to explore the extensional equivalence of perceptions of capacity and fatigue, and 2) to explore the relationship between actual capacity and the perception of that capacity. We analysed secondary outcomes from two experiments where 21 participants performed various elbow flexion tasks with either a dumbell, or a connected adaptive resistance exercise (CARE) machine enabling measurement of actual capacity (i.e., maximal force). Mixed effects ordered beta regression models estimated the latent constructs during conditions from self-reports of perceptions of capacity and fatigue comparing the two operationalisations, and the relationship between actual capacity (i.e., % maximal force) and self-reports of perceptions of capacity. We hypothesised that, given their theoretical extensional equivalence, the latent constructs captured by self-report ratings as operationalisations of perceptions of capacity and fatigue would exhibit a strong negative relationship between each other reflecting strong identity, and a positive association albeit with weak as opposed to strong identity between actual capacity and perception of capacity. Our results appear to broadly corroborate both hypotheses. There was a very strong relationship indicating strong identity and thus extensional equivalence of perceptions of capacity and fatigue latent constructs (r = -0.989 [95% CI -0.994 to -0.981]). Further, a coarse grained directional relationship between actual capacity and the perception of capacity was present suggesting only weak identity at best. Future research should endeavour to identify conditions permitting testing of assumptions of the present work (i.e., the quantity assumption) and explore further possible psychophysical models relating actual, and perceptions of, demands, capacity, and effort to understand the impact of the former upon the latter given the conceptual relationships between them.

Open Access