## 2 Materials and Methods
### Procedure  
_Sample Size Calculation._ The required sample size for this study was estimated using G*Power software (version 3.1). A priori analysis was performed to determine the minimum number of participants needed in each group to achieve a statistical power of 0.95, with a significance level (\(\alpha\)) of 0.05. The sample size calculation was based on a mixed ANOVA design with two groups and six measurement points. The results indicated that a total of 44 participants (22 by group) would be necessary to detect a medium-sized effect (f = 0.20) in the analysis. By the conclusion of the study, three participants had dropped out for various reasons, resulting in a final sample size of 49 participants (Figure 1). _Recruitment phase._ The participants were recruited by asking for volunteers in the classrooms of a secondary school. The study participants, as they were minors, were given an information sheet about the study in order for their parents or guardians to give their consent for participation. To be able to participate in the study, the participants had to meet the following requirements: a willingness to voluntarily participate in the study and submit the consent form signed by their parents or, failing that, by their legal guardian. Figure 1: Diagram illustrating the process of recruitment, group allocation, and the final selection of study participants. Those who agreed to participate in the study had to present parental authorization, after which they completed the ad hoc interview, the GSES, and the darts experience scale. Finally, they were asked to report the number of times they had played darts in the last two years. _Distribution of participants._ This process was carried out based on the scores obtained on GSES. The highest GSES score was drawn among the participants and assigned to G1 and the next highest to G2 (see Figure 1). This process was repeated until all participants were distributed into the study groups and thus matched for self-efficacy. _Manipulation of expectations._ The aim of the study was hidden from participants. To reduce the influence of demand characteristics during task performance [44], expectations about the actual aim of the study were manipulated during the volunteer recruitment phase and at the beginning of the throwing sessions. To conceal the real objective, participants were informed that the aim of the research was \"to analyze the possible influence of the presence-absence of music and the compulsory nature of music during throws (with three groups: GA--with compulsory music; GB--without compulsory music and GC--with/without music by choice) on motor performance and dart-throwing scores\". During the throws, in all cases, there was a music system present but not activated. All participants were told that they had been assigned to \"GB: without compulsory music\". To establish whether the actual goal had been successfully masked, after the completion of all throwing phases and at the end of participation, they were asked \"what do you think was the goal of the activity you have just performed?\". _Dart-throwing program._ The participants were invited to a specific classroom provided by the school after the recruitment and assignment phase. At the beginning of the first session, they were informed of the \"simulated target\" of the research and the \"supposed group\" in which they were included. After being informed, they completed the STAI before the dart-throwing phases. Then, the darts were thrown with the dominant hand. In all cases, it was the right hand, at 2.37 m from the front of the target, which was located 1.74 m from its center to the ground. The target was 42 cm in diameter with concentric circles listed from 1 to 9, with a central point of a value of 10. Before starting the dart-throwing phase, participants were asked to rank five darts based on color preference and feather pattern. To establish the baseline, the dart placed in position 2 of the ranking was taken.