I am searching for information on a countoured stereonet that is statistically well constrained in terms of the number of measurements. We used to hear that if you have more than 30 measurements you can generate a countoured diagram. Unfortunately I can't find a reference that discusses the complete statistics involved. Can anyone help?
I don't think there is a set minimum number. It would depend on the natural variability of the elements you are measuring. The only way to tell for a specific situation is to test at what number of measurements the contoured pattern stay statistically unchanged as you add more measurements. That is the data set becomes stable.
Hope this helps.
Quantity of measurements does not necessary contribute much to get good contoured diagram. More important is to have good measurements on proper outcrops and to determine relationship of measured parametres on site.
The central limit theorem tells you that "if your distribution is normal" then you need about 30 measurements to properly characterize this distribution. You have a normal or Gaussian distribution when a series of measurements are affected by many uncertainty sources. If you have less than 30 measurements then probably is best to use student's t distribution. This is also complicated by the fact that you are working with data distributed on a sphere, which will follow a von Mises distribution. Hope this is of help.
Statistics are often confusing. It depends on local arrangement, rate of deformation of rock (especially when we have few stages of deformation). If you measure monotonous rock series (f.e. granite jointing), 20-30 measurements will be enough for one plane or lineation. If you measure orientations of folds in different scales or tectonic melange, migmatites etc. you should make much more measurements (40-50 or even 100) for variable orientated planes or lineations. This will be well shown on contoured diagram, regardless using software.
I appreciate very much all the feedback provided, but I'm specially interested in the statistics discussed by Contreras.
Dr. Contreras, can you please provide us some references discussing all the statistics involved in stereographic analysis?
Dr. Perras, I couldn't find the references you cited, mainly because there are a large number of works in the web site. Can you please send the year of the publication?
These are classical results from probability theory really. Wikipedia may have decent articles about those topics. What is important, however, is that you need a distribution model for your data. The gaussian or normal distribution is only one of the many distributions a data set may obey. For example, radioactive decay follows a Poisson distribution rather than a Gaussian one. The distribution of energy in a gas follows the Boltzmann distribution. Some other times you need a distribution model for small data sets, e.g., the student's t distribution model, as the Gaussian distribution cannot handle appropriately such data sets.
In other situations the "support" of the distribution plays a role in choosing the right model. For example the Gaussian distribution has an infinite support (the tails of the distribution reach infinite), whereas directional data has a finite support that goes from 0 to 360 degrees. This is, the tails of the distribution must be contained within this support. In this latter case, it does not make a lot of sense to use a normal distribution, instead the von Mises is the right distribution to use. By the way, this kind of distribution must be treated at depth in paleomagnetism books.
Thank you Dr. Contreras, I'll try to go deeper into the complete statistics involved.
The book "Statistical Analysis of Spherical Data" by N.I. Fisher, T. Lewis, and B.J.J. Embelton addresses the statistical analysis of spherical data extremely well. It addresses in depth all of the distributions already discussed. The application of these statistics to paleomag data is describe very well in Robert Butler's "Paleomagnetism: Magnetic Domains to Geologic Terranes" book. Although no longer published, he (Butler) has placed it online at http://www.geo.arizona.edu/Paleomag/book/ Chapter 6 is most appropriate for your work. Good luck.
Thank you John. I found the chapter very helpful. I'll read it more carefully.
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