Alternate Homogeneity Calculations
The program will also calculate an alternative range of homogeneity (Meisenkothen and Donovan, 2008) based on a revised Goldstein equation that calculates the range of homogeneity in elemental weight percent expected from statistics alone (the ideal range of homogeneity) and the actual range of homogeneity in the sample. The ranges are calculated as follows:
Ideal range of homogeneity:
Actual range of homogeneity:
The only difference between the traditional Goldstein equation and the “revised” Goldstein equation is the dropping of the SQRT(n-1) term in the denominator. Leaving this term in produces homogeneity ranges that change with the number of measurements. In fact the traditional Goldstein equation is actually a measure of the standard error of the mean homogeneity.
Note that there is an alternative calculation for modeling the detection limit and/or required counting time in the program CalcZAF that is extremely useful for predicting sensitivity or analysis conditions.