Armin N. Auf der Maur (armin_adm@yahoo.com)
You may download some Excel Spreadsheets here for private and scientific use, giving due reference to the author. The text in the spreadsheets should help to use and understand them, at least partially, as the whole topic is complicated. But the application should be self-explaining.
The spreadsheet 4M.xls calculates unimodal probability functions reproducing exactly the first four moments of given data. Additionally, it contains the solution fitting the first three moments and allowing only for positive data, as described 2001 by Armin N. Auf der Maur in J. Atmos. Sci. 58, 407-418: Statistical Tools for Drop Size Distributions: Moments and Generalized Gamma. This paper showed how to solve for two parameters in a complicated transcendental function, opening the way to further applications as following here below.
The spreadsheets R.xls and R2.xls calculate the probability of the random correlation coefficient R and its square R^2, respectively, for two and three variables. The calculations are based on the first four moments of random correlation coefficients obtained from the complete set of permutations of the first (dependent) variable. This procedure corresponds to the randomization test for the null hypothesis "no correlation". It is a basis for many tests of statistical significance, replacing standard t-, F- or χ2-tests, when the assumptions associated with the latter become doubtful. The method presented here has the advantage that non linear normalizing transformations distorting the question under test can be avoided. A publication explaining more details is in preparation.
Lucerne, January 2006
