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 XIII k
Descriptive statistics of the October 10, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

3

 Eight observations of D. plexippus* and fifty seven observations of P. sennae were not included in the analysis. 

2)       Sum of sines        

-1.44314  

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

3)       Sum of cosines

-2.60474

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

4)       Mean sine

-0.48105 

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

5)       Mean cosine

-0.86825 

6)       Length of mean vector  

0.99260

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

7)       Sine of mean vector      

-0.48460  

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  

-0.87472  

9)       Angular deviation         

±8.1°

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

10)     Magnetic mean bearing

209° ±8.1°
(Southwest)

 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          

208° ±8.1°
(Southwest)

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

13)     95% confidence intervals

-

 95% Confidence Intervals (C.I.) are extrapolated from a chart using values from lines 1 and 6.

* Either no numerical record for bearing, or butterfly landed, or both for observations 449, 451, 482, 487, 510, 512, 513, and 515.  

Comments

Wind was highly variable all day.