Concept of tracer purity and its impact on the step measurement of an arbitrary quantity q. Top three panels: 400 mock data, 200 of category a (in blue), normally distributed over the quantity q by 𝒩(μ_a = 0.5, σ_a = 0.5), and 200 of category b (in orange) with a similar distribution 𝒩(μ_b = −0.5, σ_b = 0.5). The figure shows the mock q values as a function of the tracer values t for three different tracers. The data are classified as a or b given the tracer values if they are measured above or below t_cut, respectively. The top, middle, and bottom panels show tracers with perfect, medium, and null ability to track the two categories. The right panels show the tracer estimation of the q distribution for each tracer (in gray), to be compared to the true q distribution for each category (colored dashed lines). Bottom panel: evolution of the observed step γ = μ^a − μ^b, the difference of mean q values for targets classified as a or b by the tracers, as a function of the tracer contamination c = c^a + c^b; the circles show each of the three simulations illustrated in the top panels, while the line shows the prediction from Eq. (3).