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.

It is more effective to maintain good health than to regain it after losing it. This work focuses on the biochemical defense mechanisms against free radicals and their role in building and maintaining antioxidant shields, aiming to show how to balance, as much as possible, the situations in which we are exposed to free radicals. To achieve this aim, foods, fruits, and marine algae with a high antioxidant content should constitute the basis of nutritional elements, since natural products are known to have significantly greater assimilation efficiency. This review also gives the perspective in which the use of antioxidants can extend the life of food products, by protecting them from damage caused by oxidation as well as their use as food additives.

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 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.

A methodology for the design of an experiment is proposed in order to find asmany schemes as possible with the maximum number of factors with different levels for thesmallest number of experimental runs. An algorithm was developed and homemadesoftware was implemented. The abilities in generation of the largest groups of orthogonalarrays were analyzed for experimental runs of 4, 6, 8, 9, 10, 12, 14, 15, and 16. The resultsshow that the proposed method permits the construction of the largest groups of orthogonalarrays with the maximum number of factors.

One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution.