Figure 4.
The placebo test for the quadratic term beta 2 plots coefficient value on the horizontal axis and p value on the left vertical axis, with kernel density on the right vertical axis. The horizontal axis ranges from about negative 0.35 to 0.15, and the p value axis ranges from 0 to 1. Simulated p values form a narrow concentration centred near coefficient 0, rising from values near 0 at coefficients around negative 0.03 and 0.04 to about 1 near coefficient 0. The dashed kernel density estimate closely follows this distribution. A separate vertical dashed reference line appears near coefficient negative 0.33.Placebo test for quadratic term (β2)