Tactics and Vectors 98/99
                           

Home

Table of  Contents

Great Circle Hypotheis  

Magnetoclinic Hypothesis

Magnetic-Latitude Hypothesis

Compass Bearings Hypothesis

Suns' Azimuth Hypothesis

Expansion-Contraction Hypothesis

Always Advance Hypothesis

Never Go Back Hypothesis

 

 

Analysis of Field Data for the 1987 Monarch Butterfly Migration in Calhoun, Georgia

left arrowarrow leftTable II g
Descriptive statistics of the September 29, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

22

 Four obserations of  migrants of other butterfly species were not included in the analysis.

2)       Sum of sines        

-18.55707   

 Divide by sample size to get mean sine (line 4).  Also needed when pooling data from other studies.

3)       Sum of cosines

+8.92658 

Divide by sample size to get mean cosine (line 5).  Also needed when pooling data from other studies.

4)       Mean sine

-0.84350

Values for  lines 4 and 5 are used with sample size (line 1) to calculate length of mean vector (line 6).

5)       Mean cosine

+0.40575 

6)       Length of mean vector  

0.93602

 An index of  dispersal of  bearings around mean bearing.   Used to determine values for lines 9 and 13. 

7)       Sine of mean vector      

-0.90116 

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  

+0.43349  

9)       Angular deviation         

±19.9°

 Determined from Tables that convert mean vector length (line 6) into angular deviation (or circular standard deviation).

10)     Magnetic mean bearing

295.5° ±19.9°
(Northwest)

 Descriptive statistic of 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          

293.5° ±19.9°
(Northwest)

 Descriptive statistic for the True mean bearing and the dispersion around the mean for the sample.  

13)     95% confidence intervals

±8°

 Values from lines 1 and 6 are used to extrapolate 95% (or 99%) Confidence Intervals (C.I.) from appropriate Tables.

Comments

Wind was SE to S