Tactics and Vectors 98/99
                           

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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 VIII j
Descriptive statistics of the October 5, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

23

 One observation of D. plexippus* and eleven  observations  of other species (P. sennae, A. vanillae) were not included in the analysis. 

2)       Sum of sines        

-17.95667

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

3)       Sum of cosines

-8.53268

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

4)       Mean sine

-0.78072

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

5)       Mean cosine

-0.37099

6)       Length of mean vector  

0.86438

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

7)       Sine of mean vector      

-0.90321

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  

-0.42919 

9)       Angular deviation         

±30.3°

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

10)     Magnetic mean bearing

245° ±30.3°
(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          

243° ±30.3°
(Southwest)

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

13)     95% confidence intervals

±15°

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

* No numerical records for bearing for observation 281.  

Comments

Wind was variable but was mainly South to Southeast.