Graphical Evaluation of the Distribution of Small Experimental Series

Abstract

In many cases data from clinical, toxicological and other biological investigations are in the form of quantitative measurements which are arranged in groups according to the conditions under which the measured quantities are present or produced. A statistical treatment of such data is frequently required, e.g., in order to judge the certainty of the difference between the mean reactions of the individual groups, or to describe a relation between mean value and the degree of the action to which the groups have been subjected, etc. The biometric investigations of the last decades have made highly developed methods available for this purpose, but many of these statistical tests have as a necessary qualification that the numerical quantities in question must be distributed according to the normal the so-called Gaussiandistribution curve.Statistical analyses of this kind of experimental series should begin with an investigation of whether the values in each group may be assumed to show a normal distribution. For this purpose, as the present paper will demonstrate, graphical methods are available which are not only practicable, but also have the advantage of giving a n immediate idea of the mean value and standard deviation of a normal distribution.Should it be found that the numerical values in question are not normally distributed, several methods may be chosen of which two will be mentioned here; the second of these two is the most attractive from the point of view of the biologist. "he first method follows that developed by Karl Pearson: To find the type of distribution to which the material fits. Pearson's distribution types require the calculation of several parameters of higher order than the twomean and standard deviationwhich completely describe the normal

Development of a source-exposure matrix for occupational exposure assessment of electromagnetic fields in the INTEROCC study

“…To employ the reported N values in our summary statistic estimates, z Max and z Min are equated to their expected values for a sample of N quantiles z from the standard normal distribution (Zwillinger and Kokoska 2000). When the N expected values E N [ z ] are ranked according to their values, these “expected normal order statistics” [also called “rankits” by Ipsen and Jerne (1944)] are widely used in normal probability plots (Snedecor and Cochran, 1989). …”

Correlation-Based Inference for Linkage Disequilibrium With Multiple Alleles

“…For a more complete evaluation of the P-value distribution produced by a test, we propose to compute a statistic S B that adds up the squares of deviations of ordered P-values from the respective theoretical values expected under the null distribution. A visual method of plotting ordered P-values against the corresponding expected values of order statistics is known as a ''rankit plot'' (Ipsen and Jerne 1944). Such a plot very closely corresponds to the common ''Q-Q'' plot (where values are plotted against quantiles instead), unless the value of B is small.…”