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: plotly 6.7.0 | Python 3.13.13
Quality: 93/100 | Updated: 2026-05-29
"""
import os
import numpy as np
import plotly.graph_objects as go
from scipy.stats import ecdf, ks_2samp
# Theme-adaptive chrome — Imprint palette
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"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint categorical colors — semantic mapping: green=good/pass, red=bad/fail
GREEN = "#009E73" # Imprint slot 1 — Good Customers
RED = "#AE3030" # Imprint slot 5 — Bad Customers (semantic bad/fail anchor)
BLUE = "#4467A3" # Imprint slot 3 — max divergence marker
# Data — credit scoring; symmetric betas ensure ECDFs cross near score 50
np.random.seed(42)
good_customers = np.random.beta(5, 3, size=200) * 100
bad_customers = np.random.beta(3, 5, size=200) * 100
# ECDFs via scipy
good_ecdf_result = ecdf(good_customers)
bad_ecdf_result = ecdf(bad_customers)
good_sorted = good_ecdf_result.cdf.quantiles
good_cdf = good_ecdf_result.cdf.probabilities
bad_sorted = bad_ecdf_result.cdf.quantiles
bad_cdf = bad_ecdf_result.cdf.probabilities
# K-S test
ks_stat, p_value = ks_2samp(good_customers, bad_customers)
# Find point of maximum divergence
all_values = np.sort(np.concatenate([good_sorted, bad_sorted]))
good_cdf_at_all = good_ecdf_result.cdf.evaluate(all_values)
bad_cdf_at_all = bad_ecdf_result.cdf.evaluate(all_values)
diff = np.abs(good_cdf_at_all - bad_cdf_at_all)
max_idx = np.argmax(diff)
max_x = all_values[max_idx]
max_good_y = good_cdf_at_all[max_idx]
max_bad_y = bad_cdf_at_all[max_idx]
y_lo = min(max_good_y, max_bad_y)
y_hi = max(max_good_y, max_bad_y)
p_text = f"p = {p_value:.2e}" if p_value >= 0.001 else "p < 0.001"
# Figure
fig = go.Figure()
# Good Customers ECDF — Imprint green (semantic "good/pass")
fig.add_trace(
go.Scatter(
x=good_sorted,
y=good_cdf,
mode="lines",
name="Good Customers",
line={"color": GREEN, "width": 3, "shape": "hv"},
hovertemplate="<b>Good Customers</b><br>Credit Score: %{x:.1f}<br>Cumulative: %{y:.3f}<extra></extra>",
)
)
# Bad Customers ECDF — Imprint matte red (semantic "bad/fail")
fig.add_trace(
go.Scatter(
x=bad_sorted,
y=bad_cdf,
mode="lines",
name="Bad Customers",
line={"color": RED, "width": 3, "shape": "hv"},
hovertemplate="<b>Bad Customers</b><br>Credit Score: %{x:.1f}<br>Cumulative: %{y:.3f}<extra></extra>",
)
)
# Shaded region between ECDFs around point of maximum divergence
region_width = 5
region_mask = (all_values >= max_x - region_width) & (all_values <= max_x + region_width)
region_x = all_values[region_mask]
region_upper = np.maximum(good_cdf_at_all[region_mask], bad_cdf_at_all[region_mask])
region_lower = np.minimum(good_cdf_at_all[region_mask], bad_cdf_at_all[region_mask])
fig.add_trace(
go.Scatter(
x=np.concatenate([region_x, region_x[::-1]]),
y=np.concatenate([region_upper, region_lower[::-1]]),
fill="toself",
fillcolor="rgba(68,103,163,0.12)",
line={"color": "rgba(68,103,163,0.25)", "width": 1},
showlegend=False,
hoverinfo="skip",
)
)
# Maximum divergence line with diamond endpoint markers
fig.add_trace(
go.Scatter(
x=[max_x, max_x],
y=[y_lo, y_hi],
mode="lines+markers",
name=f"Max Divergence (D = {ks_stat:.3f})",
line={"color": BLUE, "width": 3, "dash": "dash"},
marker={"color": BLUE, "size": 11, "symbol": "diamond", "line": {"color": PAGE_BG, "width": 1.5}},
hovertemplate=f"<b>Max Divergence</b><br>Score: {max_x:.1f}<br>D = {ks_stat:.3f}<extra></extra>",
)
)
# K-S statistic annotation with arrow
fig.add_annotation(
x=max_x,
y=(y_lo + y_hi) / 2,
text=f"<b>K-S Statistic</b><br>D = {ks_stat:.3f}<br>{p_text}",
showarrow=True,
arrowhead=2,
arrowsize=1.0,
arrowwidth=2,
arrowcolor=BLUE,
ax=90,
ay=-40,
font={"size": 12, "color": INK, "family": "Arial, sans-serif"},
bordercolor=BLUE,
borderwidth=1.5,
borderpad=8,
bgcolor=ELEVATED_BG,
)
# Subtle dotted quartile reference lines
for y_ref in [0.25, 0.50, 0.75]:
fig.add_shape(type="line", x0=0, x1=100, y0=y_ref, y1=y_ref, line={"color": GRID, "width": 1, "dash": "dot"})
fig.update_layout(
autosize=False,
title={
"text": (
"ks-test-comparison · python · plotly · anyplot.ai"
f'<br><span style="font-size:10px;color:{INK_MUTED}">'
f"Good vs. Bad customers — distributions differ significantly "
f"(D = {ks_stat:.3f}, {p_text})</span>"
),
"font": {"size": 16, "color": INK, "family": "Arial, sans-serif"},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"title": {"text": "Credit Score (0–100)", "font": {"size": 12, "color": INK}, "standoff": 12},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": False,
"zeroline": False,
"showline": False,
"range": [-2, 102],
"dtick": 20,
},
yaxis={
"title": {"text": "Cumulative Proportion", "font": {"size": 12, "color": INK}, "standoff": 8},
"tickfont": {"size": 10, "color": INK_SOFT},
"range": [-0.02, 1.05],
"showgrid": False,
"zeroline": False,
"showline": False,
"dtick": 0.25,
"tickformat": ".2f",
},
legend={
"font": {"size": 10, "color": INK_SOFT},
"x": 0.02,
"y": 0.98,
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
margin={"l": 80, "r": 40, "t": 80, "b": 60},
hoverlabel={"font": {"size": 12}, "bgcolor": ELEVATED_BG, "bordercolor": INK_SOFT},
hovermode="x unified",
xaxis_spikemode="across",
xaxis_spikesnap="cursor",
xaxis_spikethickness=1,
xaxis_spikecolor=GRID,
xaxis_spikedash="dot",
yaxis_spikemode="across",
yaxis_spikesnap="cursor",
yaxis_spikethickness=1,
yaxis_spikecolor=GRID,
yaxis_spikedash="dot",
)
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(
f"plot-{THEME}.html",
include_plotlyjs="cdn",
config={"displayModeBar": True, "modeBarButtonsToAdd": ["drawline", "eraseshape"]},
)
Part of Kolmogorov-Smirnov Plot for Distribution Comparison on anyplot.ai.