Statistical methods median

Median partitioning is another statistical method distinct from RR The development of this methodology was driven by the need to select representative subsets from very large compound pools. Hierarchical clustering techniques... 

Application of robust statistics, especially methods of median statistics, for quantitative description of widely varying values may give information which can often be interpreted better than the results from normal parametric statistical methods. 

In addition to the usual statistical methods based on univariate descriptors (mean, median, and standard deviation) and analysis of variance, multivariate techniques of statistics and chemometrics are increasingly being used in data evaluation. Whereas the former are more rigorous in theoretical background and assumptions, the latter are useful in the presentation of the data, pattern recognition, and multivariate calibrations. Several good monographs on chemometrics are available (see for example [58-61]). 

Figure 8.3 Graphical representations of a set of n = 8 experimental values [x, = 2, 3, 5, 5, 6, 6, 7, 15]. Tr data omitting the possible outUer Xg = 15, represented by x = 4.857 and med = 5.0. Bottom all data included, represented by x = 6.125 and Xmed = 5.5. Note the relative robustness of the median value towards inclusion or not of the possible outlier. Reproduced from Meier and Ziind, Statistical Methods in Analytical Chemistry, 2nd Edition (2000), with permission of John Wiley Sons Inc.

The successive questionnaires are used to reduce the interquartile interval , a measure of the deviation of the opinion of an expert from the opinion of the whole panel (median). The aim of the first questionnaire is then to calculate this deviation. If more than one or more rounds are required, a greater consensus is to be expected on each issue (Okoh Pawlowski, 2004). According to Skulmoski et al. (2007), the process can be considered as being concluded when the answers are near the consensus, according to appropriate statistical methods. 

The simplest use of statistical methods is to provide summary parameters characterising important statistical properties of input variables and of various measures of catalyst performance (such as yield or degree of conversion), or relationships between them. Such summary parameters are usually called descriptive statistics, their common representatives are mean, median, variance, standard deviation, covariance and correlation. 

The median is not affected by outlying data, but the statistical efficiency is not good. This means that the rehability of the estimation of a dataset s population mean from a small sample of data is lower than for the other methods. 

Statistical Analysis. Analysis of variance (ANOVA) of toxicity data was conducted using SAS/STAT software (version 8.2 SAS Institute, Cary, NC). All toxicity data were transformed (square root, log, or rank) before ANOVA. Comparisons among multiple treatment means were made by Fisher s LSD procedure, and differences between individual treatments and controls were determined by one-tailed Dunnett s or Wilcoxon tests. Statements of statistical significance refer to a probability of type 1 error of 5% or less (p s 0.05). Median lethal concentrations (LCjq) were determined by the Trimmed Spearman-Karber method using TOXSTAT software (version 3.5 Lincoln Software Associates, Bisbee, AZ). 

Key Words Biological activity chemical descriptors chemical spaces classification methods compound databases decision trees diversity selection partitioning algorithms space transformation statistics statistical medians. 

The statistical tests previously described assume that the data follow a normal distribution. However, the results obtained by several analytical methods follow different distributions. These distributions are either asymmetric or symmetric but not normally distributed. In some approaches, these distributions are considered to be aberrant values superimposed on the normal distribution. In the following approach, the arithmetic mean is replaced by the median (cf. 21.1) and the standard deviation is replaced by the mean deviation, MD. 

Participation in interlaboratory comparisons and proficiency-testing programs provides additional information especially pertinent to controlling interlaboratory variation. Aliquots of homogeneous samples containing the analytes of interest are drawn and distributed to each participating laboratory. The participants results are used to calculate overall and method-specific statistics, such as means, medians, and standard devia-... 

The methods of robust statistics have recently been used for the quantitative description of series of measurements that comprise few data together with some outliers [DAVIES, 1988 RUTAN and CARR, 1988]. Advantages over classical outlier tests, such as those according to DIXON [SACHS, 1992] or GRUBBS [SCHEFFLER, 1986], occur pri-marly when outliers towards both the maximum and the minimum are found simultaneously. Such cases almost always occur in environmental analysis without being outliers in the classical sense which should be eliminated from the set of data. The foundations of robust statistics, particularly those of median statistics, are described in detail by TUKEY [1972], HUBER [1981], and HAMPEL et al. [1986] and in an overview also by DANZER [1989] only a brief presentation of the various computation steps shall be given here. 

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