28 resultados para stress analysis methods

em Aston University Research Archive


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This article explains first, the reasons why a knowledge of statistics is necessary and describes the role that statistics plays in an experimental investigation. Second, the normal distribution is introduced which describes the natural variability shown by many measurements in optometry and vision sciences. Third, the application of the normal distribution to some common statistical problems including how to determine whether an individual observation is a typical member of a population and how to determine the confidence interval for a sample mean is described.

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In this second article, statistical ideas are extended to the problem of testing whether there is a true difference between two samples of measurements. First, it will be shown that the difference between the means of two samples comes from a population of such differences which is normally distributed. Second, the 't' distribution, one of the most important in statistics, will be applied to a test of the difference between two means using a simple data set drawn from a clinical experiment in optometry. Third, in making a t-test, a statistical judgement is made as to whether there is a significant difference between the means of two samples. Before the widespread use of statistical software, this judgement was made with reference to a statistical table. Even if such tables are not used, it is useful to understand their logical structure and how to use them. Finally, the analysis of data, which are known to depart significantly from the normal distribution, will be described.

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In some studies, the data are not measurements but comprise counts or frequencies of particular events. In such cases, an investigator may be interested in whether one specific event happens more frequently than another or whether an event occurs with a frequency predicted by a scientific model.

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In any investigation in optometry involving more that two treatment or patient groups, an investigator should be using ANOVA to analyse the results assuming that the data conform reasonably well to the assumptions of the analysis. Ideally, specific null hypotheses should be built into the experiment from the start so that the treatments variation can be partitioned to test these effects directly. If 'post-hoc' tests are used, then an experimenter should examine the degree of protection offered by the test against the possibilities of making either a type 1 or a type 2 error. All experimenters should be aware of the complexity of ANOVA. The present article describes only one common form of the analysis, viz., that which applies to a single classification of the treatments in a randomised design. There are many different forms of the analysis each of which is appropriate to the analysis of a specific experimental design. The uses of some of the most common forms of ANOVA in optometry have been described in a further article. If in any doubt, an investigator should consult a statistician with experience of the analysis of experiments in optometry since once embarked upon an experiment with an unsuitable design, there may be little that a statistician can do to help.

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1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

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Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

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PCA/FA is a method of analyzing complex data sets in which there are no clearly defined X or Y variables. It has multiple uses including the study of the pattern of variation between individual entities such as patients with particular disorders and the detailed study of descriptive variables. In most applications, variables are related to a smaller number of ‘factors’ or PCs that account for the maximum variance in the data and hence, may explain important trends among the variables. An increasingly important application of the method is in the ‘validation’ of questionnaires that attempt to relate subjective aspects of a patients experience with more objective measures of vision.

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The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

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DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

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Aims: Characterization of the representative protozoan Acanthamoeba polyphaga surface carbohydrate exposure by a novel combination of flow cytometry and ligand-receptor analysis. Methods and Results: Trophozoite and cyst morphological forms were exposed to a panel of FITC-lectins. Population fluorescence associated with FITC-lectin binding to acanthamoebal surface moieties was ascertained by flow cytometry. Increasing concentrations of representative FITC-lectins, saturation binding and determination of K d and relative Bmax values were employed to characterize carbohydrate residue exposure. FITC-lectins specific for N-acetylglucosamine, N-acetylgalactosamine and mannose/glucose were readily bound by trophozoite and cyst surfaces. Minor incremental increases in FITC-lectin concentration resulted in significant differences in surface fluorescence intensity and supported the calculation of ligand-binding determinants, Kd and relative B max, which gave a trophozoite and cyst rank order of lectin affinity and surface receptor presence. Conclusions: Trophozoites and cysts expose similar surface carbohydrate residues, foremost amongst which is N-acetylglucosamine, in varying orientation and availability. Significance and Impact of the Study: The outlined versatile combination of flow cytometry and ligand-receptor analysis allowed the characterization of surface carbohydrate exposure by protozoan morphological forms and in turn will support a valid comparison of carbohydrate exposure by other single-cell protozoa and eucaryotic microbes analysed in the same manner.

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The use of quantitative methods has become increasingly important in the study of neurodegenerative disease. Disorders such as Alzheimer's disease (AD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This article reviews the advantages and limitations of the different methods of quantifying the abundance of pathological lesions in histological sections, including estimates of density, frequency, coverage, and the use of semiquantitative scores. The major sampling methods by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are also described. In addition, the data analysis methods commonly used to analyse quantitative data in neuropathology, including analyses of variance (ANOVA) and principal components analysis (PCA), are discussed. These methods are illustrated with reference to particular problems in the pathological diagnosis of AD and dementia with Lewy bodies (DLB).

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Stereology and other image analysis methods have enabled rapid and objective quantitative measurements to be made on histological sections. These mesurements may include total volumes, surfaces, lengths and numbers of cells and blood vessels or pathological lesions. Histological features, however, may not be randomly distributed across a section but exhibit 'dispersion', a departure from randomness either towards regularity or aggregation. Information of population dispersion may be valuable not only in understanding the two-or three-dimensional structure but also in elucidating the pathogenesis of lesions in pathological conditions. This article reviews some of the statistical methods available for studying dispersion. These range from simple tests of whether the distribution of a histological faeture departs significantly from random to more complex methods which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters.

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This book is aimed primarily at microbiologists who are undertaking research and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide range of data analysis methods is widely available to experimental scientists. The availability of this software, however, makes it essential that investigators understand the basic principles of statistics. Statistical analysis of data can be complex with many different methods of approach, each of which applies in a particular experimental circumstance. Hence, it is possible to apply an incorrect statistical method to data and to draw the wrong conclusions from an experiment. The purpose of this book, which has its origin in a series of articles published in the Society for Applied Microbiology journal ‘The Microbiologist’, is an attempt to present the basic logic of statistics as clearly as possible and therefore, to dispel some of the myths that often surround the subject. The 28 ‘Statnotes’ deal with various topics that are likely to be encountered, including the nature of variables, the comparison of means of two or more groups, non-parametric statistics, analysis of variance, correlating variables, and more complex methods such as multiple linear regression and principal components analysis. In each case, the relevant statistical method is illustrated with examples drawn from experiments in microbiological research. The text incorporates a glossary of the most commonly used statistical terms and there are two appendices designed to aid the investigator in the selection of the most appropriate test.

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The purlin-sheeting system has been the subject of numerous theoretical and experimental investigations over the past 30 years, but the complexity of the problem has led to great difficulty in developing a sound and general model. The primary aim of the thesis is to investigate the failure behaviours of cold-formed zed and channel sections for use in purlin-sheeting systems. Both the energy method and finite strip method are used to develop an approach to investigate cold-formed zed and channel section beams with partial-lateral restraint from the metal sheeting when subjected to a uniformly distributed transverse load. The stress analysis of cold-formed zed and channel section beams with partially-lateral restraint from the metal sheeting when subjected to a uniformly distributed transverse load is investigated firstly by using the analytical model based on the energy method in which the restraint actions of the sheeting are modelled by using two springs representing the translational and rotational restraints. The numerical results have showed that the two springs have significantly different influences on the stresses of the beams. The influence of the two springs has also been found to depend on the anti-sag bar and the position of the loading line. A novel method is presented for analysing the elastic local buckling behaviour of cold-formed zed and channel section beams with partial-lateral restraint from metal sheeting when subjected to a uniformly distributed transverse load, which is carried out by inputting the cross sectional stresses with the largest compressive stress into the finite strip analysis. By using the presented novel method, individual influences of warning stress, partially lateral restraints from the sheeting and the dimensions of the cross section and position of the loading line on the buckling behaviour are investigated.