by George F. Hart
This is a PDF article that uses the R statistical package to examine variable transformation of compositional data e.g. percentages and ppm
which suffer from the closed array problem and must be transformed prior to data analysis. Standard tests for normality, skewness and kurtosis
are illustrated. The D'Agostino test [for sample sizes 50- 1,000] and the Shapiro-Wilks test [for sample sizes of <=50] are illustrated.
Examples using the box-plot, the density histogram, density, and bag-plot functions are given.
Transformations for interval and ratio scale data are discussed with emphasis on the log-ratio transformation of Aitchison .
A procedure for transformation of ratio data for univariate and bivariate analysis is provided in which:
The percentage data is first converted to proportions by dividing them by 100. The square root of the proportion is computed,
and then the inverse sine (arcsin function) derived for the resultant proportional values.
This is a PDF article. In this study replicate samples showed general consistency but most of the variables departed from normality and needed to be transformed prior to analysis.
The eNote emphasizes graphical procedures for comparing transformed and untransformed variables and discusses variation at different levels of interest [Province, Quarry and Age of samples].
Linear discriminant function analysis [DFA] of untransformed and transformed data-frames provide probability of class [group] membership.
The eNote is support for the publication by Agha, Ferrell and Hart entitled 'Mineralogy of bentonite deposits in the northern western desert of Egypt', submitted to the journal 'Clays and Clay Minerals'.
This is a PDF article that is support for the mineralogical characteristics of the deltas of peninsular India by Hart, Ferrell, SetaRama Swamy, Banu Murthy and Gandhi.
It illustrates how an index plot can be used as a quick view to see if a particular variable is characteristic of a particular class [in this case a delta]
prior to linear discriminant function analysis [DFA].
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