AI-GEOSTATS: Log versus nscore transform

[JW]

Hello Readers,   I've followed the correspondence on the above subject with a great deal of interest. The following link http://ai-geostats.jrc.it/documents/JW_Merks/Skewed%20data%20stats.xls gives access to an Excel spreadsheet template in which a visual test for departure from normalcy is applied. This simple test, and various more advanced tests, are described in ISO/DIS 5479-Statistical interpretation of data - Tests for departure from the normal distribution. Its 1993 precursor, which derived from British Standard BS 2826 : Part 7 : 1984, does not consider  the chi-square test and the Kolmogoroff-Smirnoff test because those were deemed goodness-of-fit tests.    The formula for the variance of a general function as defined in probability theory can be used to derive the variance of the count-weighted average. Since this data set is numerically ordered, the covariance terms are irrelevant. It is simple to prove that the formula for the variance of the weighted average converges on the Central Limit Theorem as all the variable weighting factors converge on the constant weight factor of 1/n.  The template shows that the arithmetic mean of the complete set and its count-weighted average are identical. Several reiterations give increasingly more precise 95% confidence limits for the central value of the set. Degrees of freedom are no longer positive integers but positive irrationals.   This method will be discussed in detail in Sampling and Statistics Explained, a text dedicated to commonsensical sampling practices and scientifically sound statistical methods. Its Preface and Chapter 1 Introduction are already posted elsewhere. Chapter 2 Sampling Theory will be posted shortly. Of course, I appreciate feedback from ai-geostats readers so that revisions can be made if and when required.   Kind regards, Jan W Merks