# interpretation of Rayleigh test results

I have a group of bearings that appear to be clustered toward the SW. I wanted to compare this to a uniform distribution, so I selected a Rayleigh test.

Here is my code in R:

library(CircStats)

bear <- c(-113.055485, -113.055485, -113.055485, -113.055485,
-117.775314, -118.902297, -113.055485, -113.055485,
-117.775314, -121.597818, 5.130404, 5.130404,
-113.055485, -113.055485, -113.055485, -113.055485,
-178.019797, -118.902297, -118.947140, -118.947140,
-117.824638, -127.296215, -159.028166, -126.898379,
-159.028166, -159.028166, -117.150693, -125.275715,
-117.824638, -118.258142, -159.028166, -124.370972,
-118.096576, -118.096576, -118.382553, -118.096576,
-118.096576, -118.096576, 6.297989, -121.789656,
-121.896598, -126.883761, -117.150693, -117.150693,
-122.929838, -122.929838, -176.720148, -120.156298,
-127.981467, -127.981467, -119.707813, -119.707813,
-121.064324, -119.707813, -106.097798, -105.572360,
17.880409, -11.125599, 91.056381, -121.599492)

r.test(bear, degree = TRUE)

$r.bar [1] 0.8054295$p.value
[1] 1.247252e-17


My interpretation of this result is that the results are significantly oriented in a specific direction (rather than randomly around the circle). Can anyone add on that? What does the r.bar statistic indicate?

$$\bar{R}$$, or r.bar, is a measure of spread around the circle. It should be noted that:
• If $$\bar{R} = 0,$$ then the data is completely spread around the circle.
• If $$\bar{R} = 1,$$ the data is completely concentrated on one point.
$$\bar{R}$$ and sample size $$n$$ together determine the p-value of the Rayleigh test.
In your case, the $$\bar{R} = .81$$ makes it quite likely that the data is not generated from the uniform distribution around the circle.