An alternative to ordinary q-q plots: Conditional q-q plots

A comparison of fractal methods and probability plots in identifying and mapping soil metal contamination near an active mining area, Iran

Mining activities may contribute significant amounts of metals to surrounding soils. Assessing the potential effects and extent of metal contamination requires the differentiation between geogenic and additional anthropogenic sources. This study compares the use of conventional probability plots with two forms of fractal analysis (number-size and concentration-area) to separate geochemical populations of ore-related elements in agricultural area soils adjacent to Pb-Zn mining operations in the Irankuh Mountains, central Iran. The two general approaches deliver similar spatial groupings of univariate geochemical populations, but the fractal methods provide more distinct separation between populations and require less data manipulation and modeling than the probability plots. The concentration-area fractal approach was more effective than the number-size fractal and probability plotting methods at separating sub-populations within the samples affected by contamination from the mining operations. There is a general lack of association between major elements and ore-related metals in the soils. The background populations display higher relative variation in the major elements than the ore-related metals whereas near the mining operations there is far greater relative variation in the ore-related metals. The extent of the transport of contaminants away from the mine site is partly a function of the greater dispersion of Zn compared with Pb and As, however, the patterns indicate dispersion of contaminants from the mine site is via dust and not surface/groundwater. A combination of geochemical and graphical assessment, with different methods of threshold determination, is shown to be effective in separating geogenic and anthropogenic geochemical patterns.

Analysis of large and small samples of biochemical and clinical data

Statistical software often offers a list of various descriptive statistics of location and scale, but rarely selects an efficient estimate that is statistically adequate for an actual univariate sample. The sample interval estimate for a specified degree of uncertainty seems to be more meaningful if it covers an unknown value of the population parameter. The concept of an interval estimate in medicine is then used for medical decision-making. The proposed methodology, which uses the S-Plus algorithm for biochemical, biological and clinical data analysis contains the following steps: (i) Exploratory data analysis identifies basic statistical features and patterns of the data, the distributions of which are mostly non-normal, non-homogeneous and often corrupted by outliers. (ii) Sample assumptions about data, independence of sample elements, normality and homogeneity are examined. (iii) Power transformation and the Box-Cox transformation to improve sample symmetry and stabilize the spread. (iv) Classical and robust statistics for both large (n>30) and medium-sized samples (15<n<30), point and interval estimates for the parameters of location, scale and shape. For an analysis of small samples (4<n<20) the Horn procedure of pivot measures is recommended. The proposed methodology is demonstrated in two case studies, a large sample analysis of mean pregnenolone concentrations in the umbilical blood of newborns, and a small sample analysis of mean haptoglobin concentrations in human serum.

Transformation in the PC-aided biochemical data analysis

Data transformations enable expression of original data in a new scale, more suitable for data analysis. In computer-aided interactive analysis of biochemical and clinical data an exploratory data analysis often finds that the sample distribution is systematically skewed or does not accept a sample homogeneity. Under such circumstances the original data should be transformed. The power transformation and the Box-Cox transformation improve sample symmetry and also stabilize variance. Both the Hines-Hines selection graph and the plot of logarithm of a maximum likelihood function allow selection of an optimum transformation parameter. The proposed procedure of data transformation in univariate data analysis is illustrated on a determination of 17-hydroxypregnenolone in umbilical blood of a population of newborns. Lower levels of free 5-ene steroids in umbilical blood and elevated levels of 5-ene steroid sulfates indicate a congenital sex-specific placental sulfatase insufficiency. After examination of statistical assumptions by diagnostic plots of an exploratory data analysis the best estimate of a mean value of 17-hydroxypregnenolone is derived.

Graphical and statistical approaches to data analysis for in situ hybridization

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution. The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. From a theoretical perspective, the probabilistic relationship between beta-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness.(ABSTRACT TRUNCATED AT 400 WORDS)