Maintenance of positive psychological conditioning can be a key factor in eliciting high human performance. In particular, perception of error forms a causal relationship with challenges regarding task performance. Therefore, this study aimed to investigate the mediation effect of expectancy value in the relationship between the perception of error and challenge using the Phantom Model through quantitative research. This study analyzed the causal relationship between perception of error, expectancy value, and challenge in 423 young Taekwondo athletes. Frequency analysis, confirmatory factor analysis, correlation analysis, and structural equation modeling were performed on the collected data using Jamovi 1.0.1 and AMOS 23.0 statistical programs to verify the hypothesis. The challenge demonstrated a significant difference in relation to the perception of error. These results demonstrated that the perception of error not only directly affected one’s challenge but also explained the increased challenge by mediating expectations for success and subjective values. Hence, the positive perception of error increased the athletes’ expectancy value and challenge.

Background/objective: Active leisure activities like park golf are crucial for older adults' successful aging. Grounded in the Stimulus-Organism-Response (S-O-R) paradigm and Self-Determination Theory (SDT), this study investigated the structural relationships among perceived servicescape, facility image, satisfaction, motivation, and subjective well-being. Methods: A quantitative cross-sectional design was employed. Data from 264 older adult park golf participants in South Korea were analyzed using structural equation modeling. A phantom variable approach was employed to rigorously test multiple mediation effects. Results: The physical servicescape (stimulus) positively impacted both perceived image and facility satisfaction (organism), which subsequently enhanced participation motivation (response). The structural model showed an acceptable fit ( χ ² / df = 1.831, TLI = .904, CFI = .919, RMSEA = .092, SRMR = .074). Servicescape significantly predicted both image ( β = .838, p < .001) and satisfaction ( β = .699, p < .001), and image ( β = .447, p < .001) and satisfaction ( β = .299, p < .01) in turn predicted motivation, which strongly predicted subjective well-being ( β = .774, p < .001). Notably, perceived symbolic image influenced motivation more strongly than functional satisfaction. This voluntarily formed motivation then was associated with higher levels of participants' subjective well-being. Conclusion: Beyond establishing excellent physical infrastructure, fostering an emotionally appealing facility image is vital for promoting continuous sports participation and genuine psychological well-being among older adults. These findings provide empirical evidence for infrastructure design and emotion-oriented marketing in age-friendly sports facilities. Ultimately, this research offers practical insights into utilizing leisure environments as public health interventions to promote successful aging.