Compass Bearings Hypothesis
Suns' Azimuth Hypothesis
Expansion-Contraction Hypothesis
Never Go Back Hypothesis
Analysis of Field Data for the 1987 Monarch Butterfly Migration in Calhoun, Georgia
  Table XVIMean Vanishing Bearing for Danaus plexippus in East Winds Descriptive statistics for the September 28 to October 10, 1987, observations in Calhoun, Georgia |
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Statistic |
Value |
Comments |
1) Sample size |
7 |
Records with non-numerical records for vanishing bearing or wind (e.g. N instead of 360°) were not included in the analysis. |
2) Sum of sines |
-6.87388 |
Divide by sample size to get mean sine (line 4). Also needed when pooling data from other studies. |
3) Sum of cosines |
+0.47642 |
Divide by sample size to get mean cosine (line 5). Also needed when pooling data from other studies. |
4) Mean sine |
-0.98198 |
Values for lines 4 and 5 are used with sample size (line 1) to calculate length of mean vector (line 6). |
5) Mean cosine |
+0.06806 |
|
6) Length of mean vector |
0.98434 |
An index of dispersal of bearings. Used to determine values for lines 9 and 13. |
7) Sine of mean vector |
-0.99761 |
Values for lines 7 and 8 are obtained by dividing the values from lines 4 and 5 by the value for line 6. The resulting sine and cosine are used with a Trigonometry Table of sines and cosines to extrapolate the angle of the mean vector, in this case the Magnetic mean bearing (line10 ). |
8) Cosine of mean vector |
-0.06914 |
|
9) Angular deviation |
±11.5° |
Determined from Tables that convert mean vector length (line 6) into angular deviation (or circular standard deviation). |
10) Magnetic mean bearing |
274° ±11.5° |
Descriptive statistic for the True mean bearing and the dispersion around the mean for the sample. |
11) Magnetic declination |
-2ºW |
Subtract magnetic declination (variation) to obtain True bearing |
12) True mean bearing |
272° ±11.5° |
Descriptive statistic for the True mean bearing and the dispersion around the mean for the sample. |
13) 95% confidence intervals |
±10° |
95% Confidence Intervals (C.I.) are extrapolated from a chart using values from lines 1 and 6. |
Comments:
The mean vanishing bearing for D. plexippus flying in E winds in southern Ontario is 247°±32° (N = 150, CI ±5°).