Abstract:The correct application of a statistical test is directly connected with information related to the distribution of data. Anderson-Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson-Darling test is usually drawn by comparing the obtained statistic with the available critical value, which did not give any weight to the same size. This study aimed to provide a formula for calculation of p-value associated with the Anderson-Darling statistic considering the size of the sample. A Monte Carlo simulation study was conducted for sample sizes starting from 2 to 61, and based on the obtained results, a formula able to give reliable probabilities associated to the Anderson-Darling statistic is reported.
The Chi-Square test (χ2 test) is a family of tests based on a series of assumptions and is frequently used in the statistical analysis of experimental data. The aim of our paper was to present solutions to common problems when applying the Chi-square tests for testing goodness-of-fit, homogeneity and independence. The main characteristics of these three tests are presented along with various problems related to their application. The main problems identified in the application of the goodness-of-fit test were as follows: defining the frequency classes, calculating the X2 statistic, and applying the χ2 test. Several solutions were identified, presented and analyzed. Three different equations were identified as being able to determine the contribution of each factor on three hypothesizes (minimization of variance, minimization of square coefficient of variation and minimization of X2 statistic) in the application of the Chi-square test of homogeneity. The best solution was directly related to the distribution of the experimental error. The Fisher exact test proved to be the “golden test” in analyzing the independence while the Yates and Mantel-Haenszel corrections could be applied as alternative tests
Abstract:The concentration of five soil heavy metals (Pb, Co, Cr, Cu, Hg) was measured in forty sampling sites in central Transylvania, Romania, regions known as centres of pollution due to the chemical and metallurgical activities. The soil samples were collected from locations where the ground is not sliding and the probability of alluvial deposits is small. The concentration of heavy metals was measured by using the Inductively Coupled Plasma Spectrometry method. Data were verified by using the Neutron Activation Analysis method. In some locations, the concentration for the investigated heavy metals exceeds the concentration admitted by the Romanian guideline. The highest concentration of lead (1521.8 ppm) and copper (1197.6 ppm) was found in Zlatna. The highest concentration of chromium was found in Târnăveni (1080 ppm). The maximum admitted concentrations in the sensitive areas revealed to be exceed from five to forty times.
An exact probabilities method is proposed for computing the confidence limits of medical binomial parameters obtained based on the 2×2 contingency table. The developed algorithm was described and assessed for the difference between two binomial proportions (a bidimensional parameter). The behavior of the proposed method was analyzed and compared to four previously defined methods: Wald and Wilson, with and without continuity corrections. The exact probabilities method proved to be monotonic in computing the confidence limits. The experimental errors of the exact probabilities method applied to the difference between two proportions has never exceeded the imposed significance level of 5%.
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