Data analysis methods in optometry: is there a difference between two samples? Part 2.

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.

Data analysis methods in optometry. Part 5: correlation

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.

Data analysis methods in optometry Part 7: multiple linear regression

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.

Data analysis methods in optometry Part 8: Principal components analysis (PCA) and factor analysis (FA)

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.

An evaluation of task analysis techniques for industrial process control

The concept of a task is fundamental to the discipline of ergonomics. Approaches to the analysis of tasks began in the early 1900's. These approaches have evolved and developed to the present day, when there is a vast array of methods available. Some of these methods are specific to particular contexts or applications, others more general. However, whilst many of these analyses allow tasks to be examined in detail, they do not act as tools to aid the design process or the designer. The present thesis examines the use of task analysis in a process control context, and in particular the use of task analysis to specify operator information and display requirements in such systems. The first part of the thesis examines the theoretical aspect of task analysis and presents a review of the methods, issues and concepts relating to task analysis. A review of over 80 methods of task analysis was carried out to form a basis for the development of a task analysis method to specify operator information requirements in industrial process control contexts. Of the methods reviewed Hierarchical Task Analysis was selected to provide such a basis and developed to meet the criteria outlined for such a method of task analysis. The second section outlines the practical application and evolution of the developed task analysis method. Four case studies were used to examine the method in an empirical context. The case studies represent a range of plant contexts and types, both complex and more simple, batch and continuous and high risk and low risk processes. The theoretical and empirical issues are drawn together and a method developed to provide a task analysis technique to specify operator information requirements and to provide the first stages of a tool to aid the design of VDU displays for process control.

Predicting class I major histocompatibility complex (MHC) binders using multivariate statistics:comparison of discriminant analysis and multiple linear regression

The accurate in silico identification of T-cell epitopes is a critical step in the development of peptide-based vaccines, reagents, and diagnostics. It has a direct impact on the success of subsequent experimental work. Epitopes arise as a consequence of complex proteolytic processing within the cell. Prior to being recognized by T cells, an epitope is presented on the cell surface as a complex with a major histocompatibility complex (MHC) protein. A prerequisite therefore for T-cell recognition is that an epitope is also a good MHC binder. Thus, T-cell epitope prediction overlaps strongly with the prediction of MHC binding. In the present study, we compare discriminant analysis and multiple linear regression as algorithmic engines for the definition of quantitative matrices for binding affinity prediction. We apply these methods to peptides which bind the well-studied human MHC allele HLA-A*0201. A matrix which results from combining results of the two methods proved powerfully predictive under cross-validation. The new matrix was also tested on an external set of 160 binders to HLA-A*0201; it was able to recognize 135 (84%) of them.

Application of Artificial Intelligence Methods to Computer Design of Inorganic Compounds

In this paper the main problems for computer design of materials, which would have predefined properties, with the use of artificial intelligence methods are presented. The DB on inorganic compound properties and the system of DBs on materials for electronics with completely assessed information: phase diagram DB of material systems with semiconducting phases and DB on acousto-optical, electro-optical, and nonlinear optical properties are considered. These DBs are a source of information for data analysis. Using the DBs and artificial intelligence methods we have predicted thousands of new compounds in ternary, quaternary and more complicated chemical systems and estimated some of their properties (crystal structure type, melting point, homogeneity region etc.). The comparison of our predictions with experimental data, obtained later, showed that the average reliability of predicted inorganic compounds exceeds 80%. The perspectives of computational material design with the use of artificial intelligence methods are considered.

Sensitivity Analysis of Some Applied Probability Models

2000 Mathematics Subject Classi cation: Primary 90C31. Secondary 62C12, 62P05, 93C41.

Mathematical competence for information visualization by correspondence analysis methods

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

A distance education case study: A comparison of instructional delivery methods practiced by higher education faculty and emerging standards

The purpose of this research was to compare the delivery methods as practiced by higher education faculty teaching distance courses with recommended or emerging standard instructional delivery methods for distance education. Previous research shows that traditional-type instructional strategies have been used in distance education and that there has been no training to distance teach. Secondary data, however, appear to suggest emerging practices which could be pooled toward the development of standards. This is a qualitative study based on the constant comparative analysis approach of grounded theory.^ Participants (N = 5) of this study were full-time faculty teaching distance education courses. The observation method used was unobtrusive content analysis of videotaped instruction. Triangulation of data was accomplished through one-on-one in-depth interviews and from literature review. Due to the addition of non-media content being analyzed, a special time-sampling technique was designed by the researcher--influenced by content analyst theories of media-related data--to sample portions of the videotape instruction that were observed and counted. A standardized interview guide was used to collect data from in-depth interviews. Coding was done based on categories drawn from review of literature, and from Cranton and Weston's (1989) typology of instructional strategies. The data were observed, counted, tabulated, analyzed, and interpreted solely by the researcher. It should be noted however, that systematic and rigorous data collection and analysis led to credible data.^ The findings of this study supported the proposition that there are no standard instructional practices for distance teaching. Further, the findings revealed that of the emerging practices suggested by proponents and by faculty who teach distance education courses, few were practiced even minimally. A noted example was the use of lecture and questioning. Questioning, as a teaching tool was used a great deal, with students at the originating site but not with distance students. Lectures were given, but were mostly conducted in traditional fashion--long in duration and with no interactive component.^ It can be concluded from the findings that while there are no standard practices for instructional delivery for distance education, there appears to be sufficient information from secondary and empirical data to initiate some standard instructional practices. Therefore, grounded in this research data is the theory that the way to arrive at some instructional delivery standards for televised distance education is a pooling of the tacitly agreed-upon emerging practices by proponents and practicing instructors. Implicit in this theory is a need for experimental research so that these emerging practices can be tested, tried, and proven, ultimately resulting in formal standards for instructional delivery in television education. ^

Evaluation of Some Statistical Methods for the Identification of Differentially Expressed Genes

Microarray platforms have been around for many years and while there is a rise of new technologies in laboratories, microarrays are still prevalent. When it comes to the analysis of microarray data to identify differentially expressed (DE) genes, many methods have been proposed and modified for improvement. However, the most popular methods such as Significance Analysis of Microarrays (SAM), samroc, fold change, and rank product are far from perfect. When it comes down to choosing which method is most powerful, it comes down to the characteristics of the sample and distribution of the gene expressions. The most practiced method is usually SAM or samroc but when the data tends to be skewed, the power of these methods decrease. With the concept that the median becomes a better measure of central tendency than the mean when the data is skewed, the tests statistics of the SAM and fold change methods are modified in this thesis. This study shows that the median modified fold change method improves the power for many cases when identifying DE genes if the data follows a lognormal distribution.