Soru

A team of dermatological researchers is investigating a novel topical gene therapy for severe atopic dermatitis in a randomized, double-blind, vehicle-controlled clinical trial. The study is appropriately powered at $80\%$ ($\beta = 0.20$) to evaluate the primary endpoint, which is the mean change in the Eczema Area and Severity Index (EASI) score at 12 weeks.

During the design phase, the investigators pre-specify the analysis of $20$ distinct and independent secondary outcomes, including various serological cytokine levels, epidermal barrier function metrics, and sleep disruption indices. The researchers aim to maintain the overall study-wide probability of committing a Type I error at exactly $5\%$ ($\alpha = 0.05$) across the analysis of these secondary outcomes. To counteract the problem of multiple comparisons, the biostatistician applies a Bonferroni correction to adjust the significance level.

Based on this statistical design, what specific $p$-value threshold must a single secondary outcome achieve to be considered statistically significant? (Express the answer as a precise decimal).