Analysis of Count Data – Clustering – Hypotheses Testing – Plotting
In this Plot You can see how Plots can Convey Information about the Relationship between Placements:
The data for this plot comes from www.astrofaces.com. Several years ago, I went through the photos at the Astrofaces website and classed the photos by expression and by the element of the Sun, Moon, and Ascendant. The plot is of the classed data. From the plot, Fire has fewer Closed Smiles and Air has fewer Closed Frowns, otherwise, there is not much difference between the expressions.
Chernoff Faces show You Differences between Rows of data across Columns within a matrix by using Facial Expressions: (not to be confused with the expressions in the data set)
This plot is based on the data on expressions from www.astrofaces.com. (One reason I included this plot is because the expressions on the faces seem to have an astrological take – pure coincidence.) You can get Chernoff faces for your data at Vanward Statistics.
I can do Multiple Correspondence Plots for you to show Clustering for Categorical Variables:
For the Facial Expression data, the plot shows that different element / point combinations are associated with different facial expressions.
I can Model and Test Hypotheses for Astrological Questions for You, Using the Swiss Ephemeris:
In an article in Today’s Astrologer, by Cowell Jeffery, Volume 73, Number 13, Page 23, Mr. Jeffery hypothesized that if an aspect between two planets is present at birth, the same planets are likely to be in aspect at death. Mr. Jeffery used the Elizabethans Henry VIII, Queen Elizabeth I, Robert Devereux, William Cecil, and Mary Stuart, for an example. I modeled the problem for the major aspects, using an orb of 8 degrees for all of the planets and the Sun and an orb of 12 degrees for the Moon, where the planets are the eight usual planets (including Pluto, excluding Chiron).
I estimated the expected number of aspects for each point combination (there are 42 of them – I excluded aspects between Uranus, Neptune, and Pluto) – if the births and deaths occured randomly over the time period from the last decade of the 15th century to the end of the 16th century. I, also, found estimates of the variances and covariances between the point combinations. Different planetary combinations have different expected numbers of aspects and different variances and covariances. I, then, estimated the number of matches to expect, and the variance of the estimate of the number of matches to expect, if the count at birth is independent of the count at death. Using the results, I was able to test if the five Elizabethans had unusually high numbers of matches. The difference was positive but not significantly different from zero. One would need a very strong effect for the p-value of a test to be very small given a sample of five. The number seen for the Elizabethans is larger than the estimated expected count, which is encouraging, but too small to be considered significantly different from zero.
I did not tried to model seasonal, locational, or time of day patterns for the Elizabethans, which would affect the results. This is an area of ongoing research for me. Different parts of the world (or US for the US) have differing distributions of births (on which planetary placements depend) over the year, so currently I am only looking at data in localized places (in Iowa). Also, I now used the distributions of births in a data set and the seasonal patterns of births from data given to me by the State of Iowa to estimate expected counts and the covariances of the counts. I use an empirical density function generated from the birth observations to do the estimations. Since the data I am using does not have times of birth, I have not tried to account for time of day.
Links to a Vulcan Cent Ephemeris:
I have been experimenting with points I call Vulcan and Cent. The longitude of Vulcan is the average over the shortest arc of the longitudes of Ceres, Vesta, Pallas, and Juno. The declination of the point is found using the longitude and the average of the latitudes of the four. Cent is the closer midpoint of the Centaurs Chiron and Pholus – the only two civil Centaurs in Greek mythology. An ephemeris from 1900 to 2050 for the two points can be found in two files, one in rich text format and the other in pdf format. The original files I put up contained an error. The files now should be correct. I did not realize ‘abs’ was an integer function in C in computing the original function. I used the Swiss Ephemeris for the placements in longitude and latitude of Ceres, Vesta, Pallas, Juno, Chiron, and Pholus.
Here is the link: https://1drv.ms/b/s!AgjNmjy3BpFDmBBTiEPHc3qPr9ls
Earlier in this blog, there is a description of doing regression analysis with autocorrelated errors. The point Vulcan jumps 90 or 180 degrees from time to time and I look at divorce numbers (in Iowa) as related to Vulcan jumps.
For the Basics of Statistical Theory:
Gator Talk Slides
Here I have provided you with a introduction to some statistical results. Click on the link above to see the power point slides that I used for a talk to Alphee Lavoie’s AstroInvestigators. The slides cover the Normal and Chi Square distributions, plus the Central Limit Theorem, which are applied to some Astrological Data.
Sometimes, You might Find that just Plotting Astronomical Information is Interesting:
Using sidereal longitudinal limits for the constellations of the zodiac, I plotted
the placements of the zero degree points of the tropical signs within the constellations.