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.

Reactive processing methods for functionalisation of polymers and in-situ compatibilisation of poly(ethylene terephthalate)-based blends

One of the main objectives of this study was to functionalise various rubbers (i.e. ethylene propylene copolymer (EP), ethylene propylene diene terpolymer (EPDM), and natural rubber (NR)) using functional monomers, maleic anhydride (MA) and glycidyl methacrylate (GMA), via reactive processing routes. The functionalisation of the rubber was carried out via different reactive processing methods in an internal mixer. GMA was free-radically grafted onto EP and EPDM in the melt state in the absence and presence of a comonomer, trimethylolpropane triacrylate (TRlS). To optinuse the grafting conditions and the compositions, the effects of various paranleters on the grafting yields and the extent of side reactions were investigated. Precipitation method and Soxhlet extraction method was established to purifY the GMA modified rubbers and the grafting degree was determined by FTIR and titration. It was found that without TRlS the grafting degree of GMA increased with increasing peroxide concentration. However, grafting was low and the homopolymerisation of GMA and crosslinking of the polymers were identified as the main side reactions competing with the desired grafting reaction for EP and EPDM, respectively. The use of the tri-functional comonomer, TRlS, was shown to greatly enhance the GMA grafting and reduce the side reactions in terms of the higher GMA grafting degree, less alteration of the rheological properties of the polymer substrates and very little formation of polyGMA. The grafting mechanisms were investigated. MA was grafted onto NR using both thermal initiation and peroxide initiation. The results showed clearly that the reaction of MA with NR could be thermally initiated above 140°C in the absence of peroxide. At a preferable temperature of 200°C, the grafting degree was increased with increasing MA concentration. The grafting reaction could also be initiated with peroxide. It was found that 2,5-dimethyl-2,5-bis(ter-butylproxy) hexane (TIOI) was a suitable peroxide to initiate the reaction efficiently above I50°C. The second objective of the work was to utilize the functionalised rubbers in a second step to achieve an in-situ compatibilisation of blends based on poly(ethylene terephthalate) (PET), in particular, with GMA-grafted-EP and -EPDM and the reactive blending was carried out in an internal mixer. The effects of GMA grafting degree, viscosities of GMAgrafted- EP and -EPDM and the presence of polyGMA in the rubber samples on the compatibilisation of PET blends in terms of morphology, dynamical mechanical properties and tensile properties were investigated. It was found that the GMA modified rubbers were very efficient in compatibilising the PET blends and this was supported by the much finer morphology and the better tensile properties. The evidence obtained from the analysis of the PET blends strongly supports the existence of the copolymers through the interfacial reactions between the grafted epoxy group in the GMA modified rubber and the terminal groups of PET in the blends.

Quasi-lossless optical links for broad-band transmission and data processing

We present the first experimental implementation of a recently designed quasi-lossless fiber span with strongly reduced signal power excursion. The resulting fiber waveguide medium can be advantageously used both in lightwave communications and in all-optical nonlinear data processing.

Quasi-lossless spans for broadband transmission and data processing

We present the first experimental implementation of a recently designed quasi-lossless fibre span with strongly reduced signal power excursion. The resulting fibre waveguide medium can be advantageously used both in lightwave communications and in all-optical nonlinear data processing.

Quasi-lossless optical links for broad-band transmission and data processing

We present the first experimental implementation of a recently designed quasi-lossless fiber span with strongly reduced signal power excursion. The resulting fiber waveguide medium can be advantageously used both in lightwave communications and in all-optical nonlinear data processing. © 2005 IEEE.

Quasi-lossless spans for broadband transmission and data processing

We present the first experimental implementation of a recently designed quasi-lossless fibre span with strongly reduced signal power excursion. The resulting fibre waveguide medium can be advantageously used both in lightwave communications and in all-optical nonlinear data processing.

Workflow Modelling in Grid System for Satellite Data Processing

This paper focuses on a problem of Grid system decomposition by developing its object model. Unified Modelling Language (UML) is used as a formalization tool. This approach is motivated by the complexity of the system being analysed and the need for simulation model design.

Metadata and Geospatial Data Processing on the Base of XML and Grid

The software architecture and development consideration for open metadata extraction and processing framework are outlined. Special attention is paid to the aspects of reliability and fault tolerance. Grid infrastructure is shown as useful backend for general-purpose task.

Grid Infrastructure for Satellite Data Processing in Ukraine

In this paper conceptual foundations for the development of Grid systems that aimed for satellite data processing are discussed. The state of the art of development of such Grid systems is analyzed, and a model of Grid system for satellite data processing is proposed. An experience obtained within the development of the Grid system for satellite data processing in the Space Research Institute of NASU-NSAU is discussed.

Distributed Visualization Systems in Remote Sensing Data Processing Grid

Implementation of GEOSS/GMES initiative requires creation and integration of service providers, most of which provide geospatial data output from Grid system to interactive user. In this paper approaches of DOS- centers (service providers) integration used in Ukrainian segment of GEOSS/GMES will be considered and template solutions for geospatial data visualization subsystems will be suggested. Developed patterns are implemented in DOS center of Space Research Institute of National Academy of Science of Ukraine and National Space Agency of Ukraine (NASU-NSAU).

Services for Satellite Data Processing

Data processing services for Meteosat geostationary satellite are presented. Implemented services correspond to the different levels of remote-sensing data processing, including noise reduction at preprocessing level, cloud mask extraction at low-level and fractal dimension estimation at high-level. Cloud mask obtained as a result of Markovian segmentation of infrared data. To overcome high computation complexity of Markovian segmentation parallel algorithm is developed. Fractal dimension of Meteosat data estimated using fractional Brownian motion models.