Your advisor conducted a study on decision-making using a 2 (mood prime: negative, positive) × 2 (physiological arousal: adrenaline injection, saline solution injection) factorial design, and had a final sample of 80 participants. However, upon further investigation, you realized that half of participants, randomly chosen, were administered a questionnaire about their attitudes toward authority figures before the primary dependent measure, and half completed the attitudinal questionnaire after the primary dependent measure. How would you describe this design? Is it possible in this study to obtain a statistically significant 3-way interaction, even if there are no significant main effects or 2-way interactions? Do you have sufficient power to obtain a significant 3-way interaction? Is it ever appropriate to divide participants into additional groups or categories after all data have been collected? Why?