Probability distributions g_i(T) for the example of T = χ², corresponding to different spectral distribution functions f₀ (the “true” model underlying the data), f₁ (an approximation to f₀ based on finite sampling distance Δ), and f₂ (an alternative physical model of the spectrum). The calculation is made for 100 degrees of freedom and α = β = 0.025. Thus, 2.5% of the area under g₀ is to the right of the dashed vertical line, and 2.5% of the area under g₂ is to the left of this same line. Further, 5% of the area under g₁ is to the right of the vertical line.