**3. Statistical Analyses**

#### *3.1. Statistical Analyses for Behavioral Data*

Behavioral data, namely both motor response errors and speed (reaction times—RTs), underwent two separate 3-way repeated-measures ANOVAs whose factors of variability were: Respiratory conditions (2 levels: Air and Hypoxia), Cueing conditions (4 levels; NC, CC, LC and LCmot) and Target congruency (2 levels: Congruent, Incongruent). Before being submitted to the multifactorial repeated-measures ANOVA, error rate percentages were converted to arcsine values because percentage values do not exhibit homoscedasticity (e.g., [51], which is necessary for ANOVA. In fact, the distribution of percentages is binomial, whereas the arcsine transformation of the data makes the distribution normal [52].

#### *3.2. Statistical Analyses for Electrophysiological Data*

Alpha power measures were submitted to a five-way repeated–measures ANOVA with respiratory condition (R, 2 levels: Ambient-air and Hypoxia), attention cueing condition (AC, 4 levels: NC, CC, LC, and LCmot), arrows-target array congruency (C, 2 levels: Congruent and Incongruent), hemisphere (H, two levels: left hemisphere, LH, and right hemisphere, RH), and electrode (E, 4 levels; O1–O2, PO7–PO8, TPP7h–TPP8h, and F5–F6 electrode sites).

For both behavioral and electrophysiological data, the partial eta squared values (η2*p*) were systematically provided to estimate effect sizes [53,54]. Additionally, (ε) Greenhouse-Geisser correction was applied to compensate for possible violations of the sphericity assumption associated with factors which had more than two levels. The epsilon (ε) values and the corrected probability levels (in case of epsilon < 1) are reported. Post-hoc comparisons among means for significant factors with more than two levels were performed by means of Tukey HSD and/or Newman–Keuls tests.
