The application of analysis of variance (ANOVA) to different experimental designs in optometry

Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. © 2002 The College of Optometrists.

The use of analysis of variance (ANOVA) in applied microbiology

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the DF of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, it is important to consider the design of the experiment because this determines the appropriate ANOVA to use. Some of the most common experimental designs used in the biosciences and their relevant ANOVAs are discussed by. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

A method of fundamental solutions for transient heat conduction

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction. In almost all of the previously proposed MFS for time-dependent heat conduction the fictitious sources are located outside the time-interval of interest. In our case, however, these sources are instead placed outside the space domain of interest in the same manner as is done for stationary heat conduction. A denseness result for this method is discussed and the method is numerically tested showing that accurate numerical results can be obtained. Furthermore, a test example with boundary singularities shows that it is advisable to remove such singularities before applying the MFS.

A method of fundamental solutions for transient heat conduction in layered materials

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction in layered materials, where the thermal diffusivity is piecewise constant. Recently, in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction. Eng Anal Boundary Elem 2008;32:697–703], a MFS was proposed with the sources placed outside the space domain of interest, and we extend that technique to numerically approximate the heat flow in layered materials. Theoretical properties of the method, as well as numerical investigations are included.

The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.

A novel, dynamic, in vivo, non-contact method of measuring oxygen depletion rate of the anterior eye

Despite the importance of oxygen measurements, techniques have been limited by their invasive nature and small corneal area of assessment. The aim of this study was to assess a non-contact way of measuring oxygen uptake of the whole anterior eye.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Development of performance models for co-operative information systems in an organisational context

The thesis reports of a study into the effect upon organisations of co-operative information systems (CIS) incorporating flexible communications, group support and group working technologies. A review of the literature leads to the development of a model of effect based upon co-operative business tasks. CIS have the potential to change how co-operative business tasks are carried out and their principal effect (or performance) may therefore be evaluated by determining to what extent they are being employed to perform these tasks. A significant feature of CIS use identified is the extent to which they may be designed to fulfil particular tasks, or by contrast, may be applied creatively by users in an emergent fashion to perform tasks. A research instrument is developed using a survey questionnaire to elicit users judgements of the extent to which a CIS is employed to fulfil a range of co-operative tasks. This research instrument is applied to a longitudinal study of Novell GroupWise introduction at Northamptonshire County Council during which qualitative as well as quantitative data were gathered. A method of analysis of questionnaire results using principles from fuzzy mathematics and artificial intelligence is developed and demonstrated. Conclusions from the longitudinal study include the importance of early experiences in setting patterns for use for CIS, the persistence of patterns of use over time and the dominance of designed usage of the technology over emergent use.

Mechanical vibration characteristics of bell-type pump maintings

This thesis describes an analytical and experimental study to determine the mechanical characteristics of the pump mounting, bell housing type. For numerical purposes, the mount was modelled as a thin circular cylindrical shell with cutouts, stiffened with rings and stringers; the boundary conditions were considered to be either clamped-free or clamped-supporting rigid heavy mass. The theoretical study was concerned with both the static response and the free vibration characteristics of the mount. The approach was based on the Rayleigh-Ritz approximation technique using beam characteristic (axial) and trigonometric (Circumferential) functions in the displacement series, in association with the Love - Timoshenko thin shell theory. Studies were carried out to determine the effect of the supported heavy mass on the static response, frequencies and mode shapes; in addition, the effects of stringers, rings and cutouts on vibration characteristics were investigated. The static and dynamic formulations were both implemented on the Hewlett Packard 9845 computer. The experimental study was conducted to evaluate the results of the natural frequencies and mode shapes, predicted numerically. In the experimental part, a digital computer was used as an experiment controller, which allowed accurate and quick results. The following observations were made: 1. Good agreements were obtained with the results of other investigators. 2. Satisfactory agreement was achieved between the theoretical and experimental results. 3. Rings coupled the axial modal functions of the plain cylinder and tended to increase frequencies, except for the torsion modes where frequencies were reduced. Stringers coupled the circumferential modal functions and tended to decrease frequencies. The effect of rings was stronger than that of stringers. 4. Cutouts tended to reduce frequencies; in general, but this depends on the location of the cutouts; if they are near the free edge then an increase in frequencies is obtained. Cutouts coupled both axial and circumferential modal functions. 5. The supported heavy mass had similar effects to those of the rings, but in an exaggerated manner, particularly in the reduction of torsion frequencies. 6. The method of analysis was found to be a convenient analytical tool for estimating the overall behaviour of the shell with cutouts.

The impact of stressors and regulatory focus on creativity:a dual level of analysis

Presentation

A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.

A method of fundamental solutions for the one-dimensional inverse Stefan problem

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

A comparative study on applying the method of fundamental solutions to the backward heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the backward heat conduction problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct heat conduction problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.