Figure 3.
A placebo test plots simulated p values against coefficient values with a kernel density estimate and a vertical reference line for the linear term beta 1.The placebo test for the linear term beta 1 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 0.1 to above 0.2, while the p value axis ranges from 0 to 1. Simulated p values form a narrow symmetric concentration centred near coefficient 0. The values rise from near 0 at coefficients around negative 0.02 and 0.02 to about 1 at coefficient 0, then decline similarly on the opposite side. A dashed kernel density estimate closely follows this central distribution. A separate vertical dashed reference line appears near coefficient 0.23.

Placebo test for linear term (β1)

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