A notched box plot extends the standard box plot by adding notches around the median that represent a confidence interval. If the notches of two boxes do not overlap, this provides visual evidence that the medians differ significantly. This variant is particularly valuable for quick visual hypothesis testing and comparing group medians in statistical analysis.
""" anyplot.ai
box-notched: Notched Box Plot
Library: altair 6.1.0 | Python 3.13.13
Quality: 82/100 | Updated: 2026-05-07
"""
import altair as alt
import numpy as np
import pandas as pd
# Data - Employee performance scores across departments
np.random.seed(42)
departments = ["Engineering", "Marketing", "Sales", "Operations"]
data = []
# Create varied distributions to showcase notched box plot features
# Engineering: high scores, tight distribution
engineering = np.random.normal(78, 8, 80)
engineering = np.clip(engineering, 50, 100)
data.extend([{"Department": "Engineering", "Performance Score": v} for v in engineering])
# Marketing: moderate scores, wider distribution with some outliers
marketing = np.concatenate(
[
np.random.normal(68, 12, 70),
np.array([35, 38, 95, 98]), # outliers
]
)
data.extend([{"Department": "Marketing", "Performance Score": v} for v in marketing])
# Sales: bimodal-ish, high variability
sales = np.concatenate([np.random.normal(60, 10, 40), np.random.normal(80, 8, 45)])
data.extend([{"Department": "Sales", "Performance Score": v} for v in sales])
# Operations: lower median, different from Engineering (to show non-overlapping notches)
operations = np.random.normal(62, 10, 75)
operations = np.clip(operations, 30, 95)
data.extend([{"Department": "Operations", "Performance Score": v} for v in operations])
df = pd.DataFrame(data)
# Altair does not natively support notched box plots
# We need to calculate the notch values manually and use layered marks
# Calculate statistics for each group
stats_list = []
for dept in departments:
values = df[df["Department"] == dept]["Performance Score"].values
q1 = np.percentile(values, 25)
median = np.percentile(values, 50)
q3 = np.percentile(values, 75)
iqr = q3 - q1
n = len(values)
# Notch calculation: ±1.57 × IQR / √n (95% CI around median)
notch_size = 1.57 * iqr / np.sqrt(n)
notch_lower = median - notch_size
notch_upper = median + notch_size
# Whiskers at 1.5*IQR
whisker_lower = max(q1 - 1.5 * iqr, values.min())
whisker_upper = min(q3 + 1.5 * iqr, values.max())
# Find actual whisker endpoints (furthest non-outlier)
non_outliers = values[(values >= q1 - 1.5 * iqr) & (values <= q3 + 1.5 * iqr)]
whisker_lower = non_outliers.min()
whisker_upper = non_outliers.max()
# Outliers
outliers = values[(values < q1 - 1.5 * iqr) | (values > q3 + 1.5 * iqr)]
stats_list.append(
{
"Department": dept,
"q1": q1,
"median": median,
"q3": q3,
"notch_lower": notch_lower,
"notch_upper": notch_upper,
"whisker_lower": whisker_lower,
"whisker_upper": whisker_upper,
"outliers": outliers.tolist(),
}
)
stats_df = pd.DataFrame(stats_list)
# Prepare outlier data
outlier_data = []
for _, row in stats_df.iterrows():
for outlier in row["outliers"]:
outlier_data.append({"Department": row["Department"], "Performance Score": outlier})
outliers_df = pd.DataFrame(outlier_data) if outlier_data else pd.DataFrame(columns=["Department", "Performance Score"])
# Color scale - Python Blue as primary, varied for categories
colors = ["#306998", "#FFD43B", "#4B8BBE", "#E85C41"]
color_scale = alt.Scale(domain=departments, range=colors)
# Box (from Q1 to notch_lower, then notch_lower to notch_upper, then notch_upper to Q3)
# For a notched box, we draw two rectangles: lower box and upper box with a narrower waist at the notch
# Lower box: Q1 to notch_lower (full width)
lower_box = (
alt.Chart(stats_df)
.mark_bar(size=60, stroke="black", strokeWidth=2)
.encode(
x=alt.X("Department:N", title="Department", axis=alt.Axis(labelFontSize=18, titleFontSize=22, labelAngle=0)),
y=alt.Y("q1:Q", title="Performance Score"),
y2="notch_lower:Q",
color=alt.Color("Department:N", scale=color_scale, legend=None),
)
)
# Upper box: notch_upper to Q3 (full width)
upper_box = (
alt.Chart(stats_df)
.mark_bar(size=60, stroke="black", strokeWidth=2)
.encode(
x="Department:N", y="notch_upper:Q", y2="q3:Q", color=alt.Color("Department:N", scale=color_scale, legend=None)
)
)
# Notch area: narrower bar from notch_lower to notch_upper
notch_box = (
alt.Chart(stats_df)
.mark_bar(size=35, stroke="black", strokeWidth=2)
.encode(
x="Department:N",
y="notch_lower:Q",
y2="notch_upper:Q",
color=alt.Color("Department:N", scale=color_scale, legend=None),
)
)
# Median line (inside the notch)
median_line = alt.Chart(stats_df).mark_tick(color="white", size=35, thickness=3).encode(x="Department:N", y="median:Q")
# Whiskers - vertical lines
whisker_rule = (
alt.Chart(stats_df)
.mark_rule(strokeWidth=2, color="black")
.encode(x="Department:N", y="whisker_lower:Q", y2="whisker_upper:Q")
)
# Whisker caps - horizontal ticks at whisker ends
lower_cap = (
alt.Chart(stats_df).mark_tick(size=30, thickness=2, color="black").encode(x="Department:N", y="whisker_lower:Q")
)
upper_cap = (
alt.Chart(stats_df).mark_tick(size=30, thickness=2, color="black").encode(x="Department:N", y="whisker_upper:Q")
)
# Outliers
outliers_chart = (
alt.Chart(outliers_df)
.mark_point(size=120, filled=True, opacity=0.8)
.encode(
x="Department:N",
y=alt.Y("Performance Score:Q"),
color=alt.Color("Department:N", scale=color_scale, legend=None),
)
if len(outliers_df) > 0
else alt.Chart(pd.DataFrame()).mark_point()
)
# Layer all elements
chart = (
alt.layer(whisker_rule, lower_cap, upper_cap, lower_box, upper_box, notch_box, median_line, outliers_chart)
.properties(
width=1600, height=900, title=alt.Title("box-notched · altair · pyplots.ai", fontSize=28, anchor="middle")
)
.configure_axis(labelFontSize=18, titleFontSize=22, grid=True, gridOpacity=0.3)
.configure_view(strokeWidth=0)
)
# Save as PNG (4800x2700 with scale_factor=3)
chart.save("plot.png", scale_factor=3.0)
# Save interactive HTML version
chart.save("plot.html")
Part of Notched Box Plot on anyplot.ai.