Robust regression and outlier detection in the evaluation of robustness tests with different experimental designs

Robustness tests are usually based on an experimental design approach. As designed experiments generally lead to a large variability among the results, erroneous results are often not readily detected. As a consequence, the ordinary least squares (OLS) estimates of the effects of the robustness test can be biased. Here, two robustness tests are studied, which both contain a suspicious result. Moreover, simulated datasets are considered to examine the influence of the extent of the outlier as well as the influence of multiple outliers. On the one hand, different methods are applied to inspect the results of the experiments for outliers: the half-normal plot of the OLS residuals, the normal probability plot of the effects and a method, which is based on experimental design reconstruction. On the other hand, two robust regression methods are applied to calculate the effects with a minimum influence of possible outliers. The different methods are compared and it is evaluated under which circumstances they can be applied.     

Regularized MANOVA (rMANOVA) in untargeted metabolomics

Many advanced metabolomics experiments currently lead to data where a large number of response variables were measured while one or several factors were changed. Often the number of response variables vastly exceeds the sample size and well-established techniques such as multivariate analysis of variance (MANOVA) cannot be used to analyze the data.     

Alternative spectrophotometric method for standardization of chlorite aqueous solutions

The chlorite ion is the principal by-product of the treatment of drinking water by chlorine dioxide. In function of the chlorite salt instability, standard solutions of this ion need standardization by iodometric titration, which is a reliable method although labor intensive and time consuming. An alternative method to standardization of aqueous chlorite solutions, based on its direct UV absorption measurement, was presented. Besides the maximum absorption (260 nm) generally used in other studies, the minimum (239 nm) and isosbestic (248 nm) wavelengths were proposed as supplementary points to chlorite quantification and their molar absorptivity coefficients were estimated (155.2 ± 0.6, 104.5 ± 1.0 and 69.0 ± 1.2 L cm⁻¹ mol⁻¹, respectively). The direct spectrophotometric determination of chlorite could be made selectively even in the presence of high concentration of major contaminants (chorine dioxide, chloride and chlorate), being a simple and rapid method, consuming very low volume of sample and generating low quantities of laboratory wastes.     

Uncertainty calculation for calibrators of the IFCC HbA1c standardization network

Within the last decade, the IFCC HbA1c standardization network has established the metrologically highest reference measurement procedure for HbA1c testing. Based on this procedure, reference calibrators are produced which in turn provide the starting point for the standardization of the manufactures routine HbA1c assays. According to the IVD directive, the uncertainty of the reference calibrators must be calculated and reported together with their assigned values. Within this article, we elaborate the uncertainty calculation according to GUM (guide to the expression of uncertainty in measurement) in detail. Finally, the results are validated by a simulation study.     

A statistical model for the optimization of dsc performance in the evaluation of drugs for preformulation studies

Differential scanning calorimetry (DSC) is a thermal analytical tool for preformulation studies. Extrapolated melting temperature (T_P) and heat of fusion (ΔH_f) can be used as parameters for optimizing the DSC performance. Two model pharmaceuticals acetaminophen and nicotinamide are used in this study. Using a factorial design for the experimental model and matrix analysis the results, the effect of sample mass, heating rate and the nitrogen flow rate were evaluated on the ΔH_f values and T_P values. Two levels for each of the procedural variables were used as a balanced experimental design with two sample sizes, two heating rates and two nitrogen flow rates. It was found that the change in the heating rate caused significant changes in the ΔH_f values but not the T_p values for acetaminophen. However, no significant effect was found for the T_p value but ΔH_f value was affected to a certain extent for nicotinamide.     

Acetic anhydride-promoted one-pot condensation of 2,4-thiazolidinedione with bisulfite adducts of aldehydes

We describe a simple and efficient one-pot method for condensing bisulfite adducts of aromatic aldehydes directly with 2,4-thiazolidinedione catalyzed by acetic anhydride. The two main highlights of this study are the one-pot condensation of bisulfite adducts with 2,4-thiazolidinedione in non-aqueous media and the use of Design of Experiment to understand and optimize the reaction conditions. This methodology was then generalized using other active methylene compounds, such as malononitrile.     

New NIST sediment SRM for inorganic analysis

NIST maintains a portfolio of more than 1300 standard reference materials (SRM), more than a third of these relating to measurements in the biological and environmental fields. As part of the continuous renewal and replacement efforts, a set of new marine sediments has been recently developed covering organic and inorganic determinations. This paper describes the steps taken in sample preparation, homogeneity assay, and analytical characterization and certification with specific emphasis on SRM 2702 inorganics in marine sediment. Neutron activation analysis showed the SRM to be highly homogeneous, opening the possibility for use with solid sampling techniques. The certificate provides certified mass fraction values for 25 elements, reference values for eight elements, and information values for 11 elements, covering most of the priority pollutants with small uncertainties of only several percent relative. The values were obtained by combining results from different laboratories and techniques using a Bayesian statistical model. An intercomparison carried out in field laboratories with the material before certification illustrates a high commutability of this SRM.Electronic Supplementary Material Supplementary material is available in the online version of this article at     

素食人群尿液1H NMR代谢轮廓的多因素方差分析

结合方差分析(ANOVA)和偏最小二乘法判别分析(PLS-DA)两种分析技术,对素食和普食人群的尿液1H NMR谱进行分析.利用ANOVA方法将数据矩阵分解为几个独立因素矩阵,滤除干扰因素后,再利用PLS-DA对单因素数据进行建模分析.实验结果表明,ANOVA/PLS-DA方法可以有效地减少饮食因素和性别因素之间的相互...     

固体分层取样方案的最优化设计

本文首次从理论上探讨了取得量对分层取样误差的影响,提出了总取样量一定时各层的最佳取样量和最小取样方差的计算公式,从而为分层取样的最佳取样方案设计提供了理论依据。     

Statistical analysis of data from accelerated ageing tests of PES UF membranes

In this research, membrane life-time was evaluated by means of accelerated ageing experiments. A pressure pulse unit was used to perform the ageing experiments in an accelerated way. An experimental design has been set up and four ageing factors were varied at two levels. The four ageing factors studied were: fouling status of the membrane, cleaning agent concentration, magnitude of the back pulse and number of applied back pulses. The integrity of the membrane modules was evaluated by means of permeability testing, pressure decay tests and bubble tests. Also tensile tests were performed to investigate the mechanical properties of the membrane modules. The collected data was used for an analysis of variance to determine which ageing factors and which combination of ageing factors influence membrane life time. The analysis showed that the fouling status in combination with the number of applied pressure pulses were significant ageing factors. Additional tensile tests confirmed these results.     

Parallel co-ordinate geometry and principal component analysis for the interpretation of large multi-response experimental designs

In the evaluation of large or complex data sets the use of visualization methods can be of great benefit. In this paper, the use of parallel co-ordinate geometry (PCG) plots, principal component analysis (PCA) and N-way PCA as visualization procedures for large multi-response experimental designs was compared with the more traditional approach of calculating factor effects by multiple linear regression. PCG plots are a recent addition to the visualization tools and offer a possibility to visualize multi-dimensional data in two dimensions while no calculations are required. It was found that PCA and PCG each have their own benefits and disadvantages. Both methods can be used to some extent to select optimal conditions. Moreover, it was possible to use the PCA score plot as a Pareto optimality plot that allowed to select the experiments considered to be Pareto optimal. Therefore, the examined visualization methods can be useful and complementary aids in the interpretation of large multi-response experimental design data and they add a multivariate dimension to the more classical univariate analysis of such data.     

The construction of simultaneous optimal experimental designs for several polynomials in the calibration of analytical methods

In this paper a criterion is described for the construction of experimental designs for the evaluation of calibration models in analytical chemistry. The proposed criterion seeks a compromise between the D-optimal designs for estimating the parameters of different polynomial models. A computer algorithm is presented for a sequential construction of experimental designs using the optimality criterion. The performance of the optimality criterion and the computer algorithm is elaborated for the problem of discrimination between a first- to a third-degree polynomial for the calibration of analytical methods. An experimental design consisting of replicate measurements at five distinct levels equally spaced over the calibration range proved a good solution.     

Exploring Omics data from designed experiments using analysis of variance multiblock Orthogonal Partial Least Squares

Many experimental factors may have an impact on chemical or biological systems. A thorough investigation of the potential effects and interactions between the factors is made possible by rationally planning the trials using systematic procedures, i.e. design of experiments. However, assessing factors' influences remains often a challenging task when dealing with hundreds to thousands of correlated variables, whereas only a limited number of samples is available. In that context, most of the existing strategies involve the ANOVA-based partitioning of sources of variation and the separate analysis of ANOVA submatrices using multivariate methods, to account for both the intrinsic characteristics of the data and the study design. However, these approaches lack the ability to summarise the data using a single model and remain somewhat limited for detecting and interpreting subtle perturbations hidden in complex Omics datasets.     

Application of three-variables Doehlert matrix for optimisation of an on-line pre-concentration system for zinc determination in natural water samples by flame atomic absorption spectrometry

This article describes an on-line pre-concentration system for zinc determination in environmental samples by flame atomic absorption spectrometry (FAAS). It was based on the sorption of zinc(II) ions in a minicolumn of polyurethane foam loaded with 4-(2-pyridylazo)-resorcinol (PAR). The optimisation step was carried out using two-level full factorial and a Doehlert design. Three variables (sampling flow rate, buffer concentration and pH) were regarded as factors in the optimisation. Results of the two-level full factorial design 2³ for 8 runs (in duplicate) based on the Analysis of Variance (ANOVA) demonstrated that all the factors in the tested levels are statistically significant. Besides, the interaction (sampling flow rate×buffer concentration) was also statistically significant. A three-variables Doehlert design was applied in order to determine the best condition for pre-concentration and determination of zinc. The validation process was assessed as: parameters of the analytical curve, precision, effect of other ions in the proposed system, robustness test and accuracy. The proposed system allowed determination of zinc with detection limit (3σ/S) of 0.28 μg l⁻¹, and a precision (reproducibility), calculated as relative standard deviation (R.S.D.) of 10.0 and 3.7% for zinc concentration of 1.0 and 5.0 μg l⁻¹, respectively. The achieved pre-concentration factor was 91.23 and the sampling frequency was 48 samples per hour. The achieved recovery for zinc determination in presence of several cations demonstrated that this procedure could be applied for analysis of water samples. The accuracy was confirmed by analysis of three certified reference materials. This procedure was applied for zinc determination in several kinds of water samples including saline aqueous waste from oil Refinery.     

Hierarchical classification designs for the estimation of different sources of variability in proficiency testing experiments

An approach to the estimation of possible different sources of variation found in proficiency testing experiments is described. Four errors namely, technique, analyst, laboratory and geographical location are considered and calculated by using a rational experimental design based on hierarchical classification. The treatment of the confidence of the design over different experimental arrangements is explored and visualised by calculating a function that depends only on the design and not on the experimental response. An illustrative example based on simulated data is used to show how the theory could be applied in practice.     

The new approach of standardization of capillary electrophoresis

In this paper, we develope the new standardization methods to eliminate the influence in capillary electrophoresis (CE). The markers were used to determine the basis position and then correct the data of sample by the migration time of standard sample, and make the migration time of samples consistent with the standard sample by the criterion of the marker. The problem of time transition was corrected in this way. Then according to the peak height or peak area of the marker in the sample (peak height was used here) compared with the standard sample, the sample data was zoomed appropriately. The absorbance error was made to be correct. The wavelet de-noise method was also used to make the data smooth and get a good baseline.     

The Hartree–Fock triplet instability: influence of conformation and substitution

The triplet Hartree–Fock (HF) instability is investigated through the examples of substituted ethylenes and the small linear conjugated systems butadiene, hexatriene, octatetraene. A statistical analysis is performed for several conformations of the latters. The second eigenvalue of the instability matrix appears to be able to discriminate the groups of unsaturated compounds. The HF instability is largely influenced by conjugation and mesomeric effects and thus by the geometry. The number of π electrons is also an important factor. The electronic correlation related to the HF instability is not quantified by the energy difference between the post-HF and HF levels.     

Uncertainty calculations in the certification of reference materials

To serve as a measurement standard, a (certified) reference material must be stable. For this purpose, the material should undergo stability testing after it has been prepared. This paper looks at the statistical aspects of stability testing. Essentially, these studies can be described with analysis of variance statistics, including variant regression analysis. The latter is used in practice for both trend analysis and for the development of expressions for extrapolations. Extrapolation of stability data is briefly touched upon, as far as the combined standard uncertainty of the reference material is concerned. There are different options to validate the extrapolations made from initial stability studies, and some of them might influence the uncertainty of the reference material and/or the shelf-life. The latter is the more commonly observed consequence of what is called ’stability monitoring’. Received: 6 October 2000 Accepted: 4 December 2000     

系列Fe4S4簇合物的光谱分析

本文报道了自合成的4种类立方烷型Fe_4S_4簇合物[Et_4N][Fe_4S_4(Et_2dtc)_4]、[Et_4N]_2·[Fe_4S_4(Et_2dtc)_4]、[Et_4N]_3[Fe_4S_4(Et_2dtc)_4]、[Bu_4N]_2[Fe_4S_4(PhS)_4]的UV-Vis和IR光谱数据,对照X光衍射测定结果,依据配体场弱场理论,对各光谱进行了分析和指认。讨论了配离子构型、中心离子氧化态对d-d带和荷迁移带的影响及键长、配位环境等几何因素与振动带的关系。