Hello Amit,

ISO Technical Committee 69 - Applications of Statistical Methods, had developed several standards to verify whether or not a data set departs significantly from the normal probability distribution by applying tests for kurtosis and skweness, or Shapiro-Wilk and Epps-Pulley tests. A simple test is to look at the logarithms of the ordered data set and see how much the plot departs from a straight line.

The count-weighted average and the variance of two or more sets are easy to calculate. However, calculating confidence limits for the count-weighted average is more complicated. The first step is to divide the ordered set into subsets such that each converges on a straight-line segment of the log plot, and to calculate for all subsets the count-weighted average, its variance and 95% confidence limits. The second step is to divide all subsets into pairs and repeat the calculations. The count-weighted average remains the same but its variance and 95% confidence limits change and the number of degrees of freedom increases.

Theoretically, this process could be repeated until all subsets contain a single pair of data. What it does do is recover degrees of freedom that are lost due to the grouping of data and thus gives lower t-values. Since you are a novice in stats and degrees of freedom are elusive entities without mass or temperature, I've sent you an Excel file with a numerical example of this reiterative calculation. You'll see that the precision of the central value of a data set that departs significantly from the normal distribution is low but at least it is an unbiased estimate.

Kind regards,

Jan W Merks



l ■

Hello Jan ,

Thank you.This topic grabed my attention since I have little backgroud in stats as well and I am interested in the same subject. I was wondering if you can send me the excel file as well.

It would be also great if you can direct me to a source to read a little more on this subject. I have your Metrology in Mining and Metallurgy book in hand , is there ant chapter you have mentioned about this topic in the book?

Regards ,

Hamed ■

Howdy Hamed,

Download http://geostatscam.com/Adobe/Chapter...ingTheory.pdf

Look under Multinomial probability distribution. Multimodal distributions are altogether different.

JanWMerks ■

Hello Jan,

Thanks a lot for your quick response!

Regards,

Hamed ■