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 I b
Population Mean Direction:  Calculations

Calulations of  mean direction and other descriptive statistics for the Sept. 28 - Oct. 10  Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

327

 Based on Category I Vanishing Bearings.  Analysis restricted to data with a numerical value for bearing.

2)       Sum of sines        

-112.36333 

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

3)       Sum of cosines

-164.94147

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

4)       Mean sine

-0.34362

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

5)       Mean cosine

-0.50441

6)       Length of mean vector  

0.61033

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

7)       Sine of mean vector      

-0.56301

 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  

-0.82645

9)       Angular deviation         

±50.6°

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

10)     Magnetic mean bearing

214° ±50.6°
(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          

212° ±50.6°
(Southwest)

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

13)     95% confidence intervals

±8°

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

Comments

  1. Population Mean Direction for the Georgia, 1987, differs from that of  southern Ontario migrants (222° ±51°, and CI = ±5°).   However, a two-sample statistical tests is necessary to see if observed difference is significant.

  2. The 95% Confidence Intervals for the Population Mean Direction (212 + 8 = 220°) did not include the 226.2° Great Circle direction to the overwintering sites from Calhoun.