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: letsplot 4.10.1 | Python 3.13.13
Quality: 90/100 | Updated: 2026-05-29
"""
import os
import numpy as np
import pandas as pd
from lets_plot import (
LetsPlot,
aes,
arrow,
coord_cartesian,
element_blank,
element_line,
element_markdown,
element_rect,
element_text,
geom_ribbon,
geom_segment,
geom_step,
geom_text,
ggplot,
ggsave,
ggsize,
labs,
layer_tooltips,
scale_color_manual,
scale_x_continuous,
scale_y_continuous,
theme,
theme_minimal,
)
from scipy import stats
LetsPlot.setup_html()
# Theme tokens — Imprint palette chrome (theme-adaptive)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint categorical palette — hybrid-v3 sort
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
ANYPLOT_AMBER = "#DDCC77" # warning / caution semantic anchor (outside categorical pool)
# Data — credit scoring: Good vs Bad customer score distributions
np.random.seed(42)
good_scores = np.clip(np.random.normal(loc=620, scale=80, size=500), 300, 850)
bad_scores = np.clip(np.random.normal(loc=520, scale=90, size=300), 300, 850)
# Compute ECDFs
good_sorted = np.sort(good_scores)
good_ecdf = np.arange(1, len(good_sorted) + 1) / len(good_sorted)
bad_sorted = np.sort(bad_scores)
bad_ecdf = np.arange(1, len(bad_sorted) + 1) / len(bad_sorted)
# K-S test
ks_stat, p_value = stats.ks_2samp(good_scores, bad_scores)
# Find point of maximum divergence
all_values = np.sort(np.concatenate([good_sorted, bad_sorted]))
good_ecdf_all = np.searchsorted(good_sorted, all_values, side="right") / len(good_sorted)
bad_ecdf_all = np.searchsorted(bad_sorted, all_values, side="right") / len(bad_sorted)
max_idx = np.argmax(np.abs(good_ecdf_all - bad_ecdf_all))
max_x = all_values[max_idx]
max_good_y = good_ecdf_all[max_idx]
max_bad_y = bad_ecdf_all[max_idx]
ks_mid_y = (max_good_y + max_bad_y) / 2
# DataFrames for ggplot layers
df_good = pd.DataFrame({"score": good_sorted, "ecdf": good_ecdf, "group": "Good Customers"})
df_bad = pd.DataFrame({"score": bad_sorted, "ecdf": bad_ecdf, "group": "Bad Customers"})
df_ecdf = pd.concat([df_good, df_bad], ignore_index=True)
ribbon_ymin = np.minimum(good_ecdf_all, bad_ecdf_all)
ribbon_ymax = np.maximum(good_ecdf_all, bad_ecdf_all)
df_ribbon = pd.DataFrame({"score": all_values, "ymin": ribbon_ymin, "ymax": ribbon_ymax})
df_ks_seg = pd.DataFrame(
{"x": [max_x], "y": [min(max_good_y, max_bad_y)], "xend": [max_x], "yend": [max(max_good_y, max_bad_y)]}
)
df_ks_arrow = pd.DataFrame({"x": [max_x + 40], "y": [ks_mid_y + 0.06], "xend": [max_x + 3], "yend": [ks_mid_y]})
df_ks_label = pd.DataFrame({"score": [max_x + 42], "ecdf": [ks_mid_y + 0.08], "label": [f"D = {ks_stat:.3f}"]})
# Subtitle with formatted K-S stats (element_markdown renders the bold/span tags)
subtitle_text = (
f"K-S Statistic: **{ks_stat:.3f}** | "
f"p-value: **{p_value:.2e}** "
f"<span style='color:{INK_MUTED}'>(highly significant)</span>"
)
title = "ks-test-comparison · python · letsplot · anyplot.ai"
# Ribbon: amber on light (caution semantic), neutral-muted on dark (amber+dark = olive)
ribbon_color = ANYPLOT_AMBER if THEME == "light" else INK_MUTED
ribbon_alpha = 0.20 if THEME == "light" else 0.30
# Plot
plot = (
ggplot(df_ecdf, aes(x="score", y="ecdf"))
# Ribbon shows total divergence area (amber on light = caution; muted on dark = neutral)
+ geom_ribbon(
data=df_ribbon,
mapping=aes(x="score", ymin="ymin", ymax="ymax"),
fill=ribbon_color,
alpha=ribbon_alpha,
tooltips="none",
)
# Both ECDFs as step functions — Imprint positions 1 (green) and 3 (blue)
+ geom_step(
mapping=aes(color="group"),
size=2.2,
tooltips=layer_tooltips()
.line("@group")
.line("Score|@score")
.line("ECDF|@ecdf")
.format("@score", ".0f")
.format("@ecdf", ".3f"),
)
# Dashed red segment at maximum divergence
+ geom_segment(
data=df_ks_seg,
mapping=aes(x="x", y="y", xend="xend", yend="yend"),
color=IMPRINT_PALETTE[4],
size=2.5,
linetype="dashed",
tooltips="none",
)
# Arrow pointing from annotation label to K-S midpoint
+ geom_segment(
data=df_ks_arrow,
mapping=aes(x="x", y="y", xend="xend", yend="yend"),
color=IMPRINT_PALETTE[4],
size=1.2,
arrow=arrow(length=8, type="closed"),
tooltips="none",
)
# Bold annotation of K-S statistic value — ink color for readability on both themes
+ geom_text(
data=df_ks_label,
mapping=aes(x="score", y="ecdf", label="label"),
color=INK,
size=5,
fontface="bold",
tooltips="none",
)
+ scale_color_manual(
values={
"Good Customers": IMPRINT_PALETTE[0], # brand green
"Bad Customers": IMPRINT_PALETTE[2], # blue
}
)
+ labs(x="Credit Score (points)", y="Cumulative Proportion", title=title, subtitle=subtitle_text, color="")
+ coord_cartesian(xlim=[280, 860])
+ scale_x_continuous(breaks=list(range(300, 851, 100)))
+ scale_y_continuous(limits=[0, 1.05], breaks=[0, 0.25, 0.5, 0.75, 1.0])
+ ggsize(800, 450)
+ theme_minimal()
+ theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_border=element_blank(),
plot_title=element_text(size=16, face="bold", color=INK),
plot_subtitle=element_markdown(size=12, color=INK_SOFT),
axis_title=element_text(size=12, face="bold", color=INK),
axis_text=element_text(size=10, color=INK_SOFT),
legend_text=element_text(size=10, color=INK_SOFT),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_position="top",
panel_grid_major_x=element_blank(),
panel_grid_major_y=element_line(color=INK_SOFT, size=0.3, linetype="dashed"),
panel_grid_minor=element_blank(),
axis_line_x=element_line(color=INK_SOFT, size=0.5),
axis_line_y=element_line(color=INK_SOFT, size=0.5),
plot_margin=[40, 20, 20, 20],
)
)
# Save PNG (3200×1800 via scale=4) and HTML with interactive tooltips
ggsave(plot, f"plot-{THEME}.png", path=".", scale=4)
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Kolmogorov-Smirnov Plot for Distribution Comparison on anyplot.ai.