Tactics and Vectors analysis of field data georgia 87 III u

Tactics and Vectors 98/99

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 III u Descriptive statistics of the September 30, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia
Statistic	Value	Comments
1) Sample size	104	*Thirteen observations of D. plexippus and 21 observations of other migratory species were not included in the analysis.
2) Sum of sines	-14.65939	Divide by sample size to get mean sine (line 4). Also needed when pooling data from other studies.
3) Sum of cosines	-94.06332	Divide by sample size to get mean cosine (line 5). Also needed when pooling data from other studies.
4) Mean sine	-0.14096	Values for lines 4 and 5 are used with sample size (line 1) to calculate length of mean vector (line 6).
5) Mean cosine	-0.90446
6) Length of mean vector	0.91537	An index of dispersal of bearings. Used to determine values for lines 9 and 13.
7) Sine of mean vector	-0.15399	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	-0.98807
9) Angular deviation	±22.9°	Determined from Tables that convert mean vector length (line 6) into angular deviation (or circular standard deviation).
10) Magnetic mean bearing	189° ±22.9°	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	187° ±22.9°	Descriptive statistic for the True mean bearing and the dispersion around the mean for the sample.
13) 95% confidence intervals	±3°	95% Confidence Intervals (C.I.) are extrapolated from a chart using values from lines 1 and 6.

* No numerical records for bearing.

Comments

There was a north wind for the entire day.