XIANG YE / BAYESIAN RESEARCH

Directional
Statistics.

When the data have
a sense of direction.

Angles on a circle. Directions on a sphere. Statistical methods that respect the geometry of the data.

Explore the introduction Read the tutorials

01 / THE CIRCLE

359° and 1° are only 2° apart.
The end of the scale meets the beginning.

ANGULAR OBSERVATIONSS¹ / 001

Frequency Mean direction Observations

Observations120

Mean direction · μ67.5°

Resultant length · R̄0.65

Illustrative data · 16 equal bins · sector area ∝ count
0° at north; angles increase clockwise.

View the counts and scale

Radius ∝ √count. Outer grid ring: 29 observations. Inner rings: 25%, 50%, and 75% of that count. The count scale adapts to the largest bin. At R̄ = 1 the observation marks overlap.

Counts in 22.5° angular bins
Bearing	Count
0.0–22.5°	6
22.5–45.0°	13
45.0–67.5°	29
67.5–90.0°	29
90.0–112.5°	13
112.5–135.0°	6
135.0–157.5°	4
157.5–180.0°	3
180.0–202.5°	2
202.5–225.0°	1
225.0–247.5°	2
247.5–270.0°	2
270.0–292.5°	1
292.5–315.0°	2
315.0–337.5°	3
337.5–360.0°	4

DIRECTIONAL DATA IN

Wind & weather

↗

Animal movement

↗

Geological orientation

↗

Time & phase

01 / UNDERSTAND THE GEOMETRY

A circle has
no natural beginning.

Compass bearings and times of day wrap around. Averaging their numerical labels can be misleading: the arithmetic mean of 359° and 1° is 180°, while their circular mean is 0°.

A rose diagram makes the pattern visible by grouping observations into angular sectors. In the diagram above, larger sector areas mean more observations.

How to read a rose diagram

ON A STRAIGHT SCALE