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: ggplot2 3.5.1 | R 4.4.1
#' Quality: 90/100 | Created: 2026-05-29
library(ggplot2)
library(dplyr)
library(scales)
library(ragg)
set.seed(42)
# Theme tokens — Imprint palette
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
IMPRINT_PALETTE <- c(
"#009E73", # 1 — brand green
"#C475FD", # 2 — lavender
"#4467A3", # 3 — blue
"#BD8233", # 4 — ochre
"#AE3030", # 5 — matte red
"#2ABCCD", # 6 — cyan
"#954477", # 7 — rose
"#99B314" # 8 — lime
)
# Data: credit scoring — Good vs Bad customer score distributions
n_good <- 500
n_bad <- 500
good_scores <- rnorm(n_good, mean = 680, sd = 60)
bad_scores <- rnorm(n_bad, mean = 580, sd = 80)
# Kolmogorov-Smirnov test
ks_result <- ks.test(good_scores, bad_scores)
# Find K-S statistic location — maximum vertical distance between ECDFs
all_x <- sort(unique(c(good_scores, bad_scores)))
ecdf_good <- ecdf(good_scores)
ecdf_bad <- ecdf(bad_scores)
good_vals <- ecdf_good(all_x)
bad_vals <- ecdf_bad(all_x)
diffs <- abs(good_vals - bad_vals)
max_idx <- which.max(diffs)
ks_x <- all_x[max_idx]
ks_y_lo <- min(good_vals[max_idx], bad_vals[max_idx])
ks_y_hi <- max(good_vals[max_idx], bad_vals[max_idx])
ks_y_mid <- (ks_y_lo + ks_y_hi) / 2
# Annotation text
ks_d <- round(as.numeric(ks_result$statistic), 3)
ks_p_fmt <- formatC(ks_result$p.value, format = "e", digits = 2)
annot <- paste0("D = ", ks_d, "\np = ", ks_p_fmt)
# Long-format data frame for stat_ecdf
df_scores <- data.frame(
score = c(good_scores, bad_scores),
group = factor(
c(rep("Good Customers", n_good), rep("Bad Customers", n_bad)),
levels = c("Good Customers", "Bad Customers")
)
)
# K-S segment data frame
ks_seg <- data.frame(x = ks_x, xend = ks_x, y = ks_y_lo, yend = ks_y_hi)
# Plot
p <- ggplot(df_scores, aes(x = score, color = group, linetype = group)) +
stat_ecdf(geom = "step", linewidth = 1.2, pad = FALSE) +
geom_segment(
data = ks_seg,
aes(x = x, xend = xend, y = y, yend = yend),
color = INK,
linewidth = 0.9,
linetype = "dotdash",
inherit.aes = FALSE
) +
annotate(
"label",
x = ks_x + 22,
y = ks_y_mid,
label = annot,
color = INK,
fill = ELEVATED_BG,
size = 3.0,
hjust = 0,
label.padding = unit(0.4, "lines"),
label.size = 0.25,
label.r = unit(0.12, "lines")
) +
scale_color_manual(
name = NULL,
values = c("Good Customers" = IMPRINT_PALETTE[1],
"Bad Customers" = IMPRINT_PALETTE[2])
) +
scale_linetype_manual(
name = NULL,
values = c("Good Customers" = "solid", "Bad Customers" = "longdash")
) +
scale_y_continuous(
labels = percent_format(accuracy = 1),
limits = c(0, 1),
expand = expansion(mult = c(0.01, 0.03))
) +
scale_x_continuous(expand = expansion(mult = c(0.02, 0.06))) +
labs(
title = "ks-test-comparison · r · ggplot2 · anyplot.ai",
x = "Credit Score",
y = "Cumulative Proportion"
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = INK_SOFT, linewidth = 0.2),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
axis.line = element_line(color = INK_SOFT, linewidth = 0.4),
plot.title = element_text(color = INK, size = 12,
face = "bold",
margin = margin(b = 10)),
plot.margin = margin(t = 16, r = 24, b = 12, l = 12),
legend.background = element_rect(fill = ELEVATED_BG, color = INK_SOFT,
linewidth = 0.3),
legend.text = element_text(color = INK_SOFT, size = 8),
legend.title = element_text(color = INK, size = 10),
legend.position = "bottom",
legend.key.width = unit(1.5, "cm")
)
# Save
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/ks-test-comparison/ggplot2/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": "r",
"library": "ggplot2",
"page": "https://anyplot.ai/ks-test-comparison/r/ggplot2",
"hub": "https://anyplot.ai/ks-test-comparison",
"code_json": "https://api.anyplot.ai/specs/ks-test-comparison/ggplot2/code",
"spec_json": "https://api.anyplot.ai/specs/ks-test-comparison",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/ks-test-comparison/r/ggplot2/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/ks-test-comparison/r/ggplot2/plot-dark.png",
"quality_score": 90.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Kolmogorov-Smirnov Plot for Distribution Comparison on anyplot.ai.