A Kolmogorov-Smirnov (K-S) plot compares two empirical cumulative distribution functions (ECDFs) and visualizes the K-S statistic, which is the maximum vertical distance between the two distributions. The plot displays both ECDFs as step functions, highlights the point of maximum divergence, and typically reports the K-S statistic value and p-value for hypothesis testing. This visualization is essential for determining whether two samples come from the same underlying distribution.
# anyplot.ai
# ks-test-comparison: Kolmogorov-Smirnov Plot for Distribution Comparison
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 88/100 | Created: 2026-05-29
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const IMPRINT_PALETTE = [
colorant"#009E73",
colorant"#C475FD",
colorant"#4467A3",
colorant"#BD8233",
colorant"#AE3030",
colorant"#2ABCCD",
colorant"#954477",
colorant"#99B314",
]
# Data — credit scoring: Good vs Bad customer score distributions
n_good = 400
n_bad = 400
good_scores = randn(n_good) .* 60.0 .+ 620.0
bad_scores = randn(n_bad) .* 70.0 .+ 490.0
sorted_good = sort(good_scores)
sorted_bad = sort(bad_scores)
# KS statistic (inline — two-sample D and its x-location)
all_pts = sort(unique(vcat(sorted_good, sorted_bad)))
diffs = abs.(searchsortedlast.(Ref(sorted_good), all_pts) ./ n_good .-
searchsortedlast.(Ref(sorted_bad), all_pts) ./ n_bad)
ks_idx = argmax(diffs)
ks_d = diffs[ks_idx]
ks_x = all_pts[ks_idx]
# KS p-value (asymptotic Kolmogorov distribution, inline)
n_eff = sqrt((n_good * n_bad) / (n_good + n_bad))
z = ks_d * (n_eff + 0.12 + 0.11 / n_eff)
ks_p = max(0.0, min(1.0, 2.0 * sum((-1)^(k - 1) * exp(-2.0 * k^2 * z^2) for k in 1:100)))
# CDF values at the KS point for the gap segment
cdf_good_at_ks = searchsortedlast(sorted_good, ks_x) / n_good
cdf_bad_at_ks = searchsortedlast(sorted_bad, ks_x) / n_bad
y_lo = min(cdf_good_at_ks, cdf_bad_at_ks)
y_hi = max(cdf_good_at_ks, cdf_bad_at_ks)
# ECDF step function coordinates
function ecdf_step(sv)
n = length(sv)
xs = vcat(sv[1] - 5.0,
vec(permutedims(hcat(sv, sv))),
sv[end] + 5.0)
ys = vcat(0.0,
vec(permutedims(hcat((0:n-1) ./ n, (1:n) ./ n))),
1.0)
return xs, ys
end
xs_good, ys_good = ecdf_step(sorted_good)
xs_bad, ys_bad = ecdf_step(sorted_bad)
# Dense x grid for band fill (evaluates both ECDFs at every data point)
x_fill = sort(unique(vcat(sorted_good, sorted_bad)))
y_good_fill = [searchsortedlast(sorted_good, x) / n_good for x in x_fill]
y_bad_fill = [searchsortedlast(sorted_bad, x) / n_bad for x in x_fill]
# Title
title_str = "ks-test-comparison · julia · makie · anyplot.ai"
title_size = max(14, round(Int, 20 * min(1.0, 67.0 / length(title_str))))
# Plot
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = title_str,
titlesize = title_size,
titlecolor = INK,
xlabel = "Credit Score",
ylabel = "Cumulative Proportion",
xlabelsize = 14,
ylabelsize = 14,
xticklabelsize = 12,
yticklabelsize = 12,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = RGBAf(INK.r, INK.g, INK.b, 0.12),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.12),
xminorgridvisible = false,
yminorgridvisible = false,
limits = (nothing, nothing, -0.02, 1.05),
)
# Shaded fill between ECDF curves (narrates the divergence region)
ks_red = IMPRINT_PALETTE[5]
band!(ax, x_fill, min.(y_good_fill, y_bad_fill), max.(y_good_fill, y_bad_fill);
color = RGBAf(ks_red.r, ks_red.g, ks_red.b, 0.12))
# ECDFs
lines!(ax, xs_good, ys_good;
color = IMPRINT_PALETTE[1], linewidth = 2.5, label = "Good Customers")
lines!(ax, xs_bad, ys_bad;
color = IMPRINT_PALETTE[2], linewidth = 2.5, label = "Bad Customers")
# KS statistic: dashed vertical marker + filled gap segment
vlines!(ax, [ks_x]; color = IMPRINT_PALETTE[5], linewidth = 1.2, linestyle = :dash)
lines!(ax, [ks_x, ks_x], [y_lo, y_hi];
color = IMPRINT_PALETTE[5], linewidth = 4.0)
# Annotation: D value and p-value
ks_p_str = ks_p < 0.001 ? "p < 0.001" : "p = $(round(ks_p; digits = 3))"
text!(ax,
"D = $(round(ks_d; digits = 3))\n$(ks_p_str)";
position = Point2f(ks_x + 8.0, (y_lo + y_hi) / 2.0),
align = (:left, :center),
color = INK,
fontsize = 16,
)
axislegend(ax;
position = :rb,
labelsize = 12,
framevisible = true,
framecolor = INK_SOFT,
backgroundcolor = ELEVATED_BG,
labelcolor = INK,
)
# Save
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/ks-test-comparison/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "ks-test-comparison",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/ks-test-comparison/julia/makie",
"hub": "https://anyplot.ai/ks-test-comparison",
"code_json": "https://api.anyplot.ai/specs/ks-test-comparison/makie/code",
"spec_json": "https://api.anyplot.ai/specs/ks-test-comparison",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/ks-test-comparison/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/ks-test-comparison/julia/makie/plot-dark.png",
"quality_score": 88.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Kolmogorov-Smirnov Plot for Distribution Comparison on anyplot.ai.