Development and psychometric evaluation of the spirituality instrument (SpI-27) in a sample of people with chronic illness

Background: Spirituality is fundamental to all human beings, existing within a person, and developing until death. This research sought to operationalise spirituality in a sample of individuals with chronic illness. A review of the conceptual literature identified three dimensions of spirituality: connectedness, transcendence, and meaning in life. A review of the empirical literature identified one instrument that measures the three dimensions together. Yet, recent appraisals of this instrument highlighted issues with item formulation and limited evidence of reliability and validity. Aim: The aim of this research was to develop a theoretically-grounded instrument to measure spirituality – the Spirituality Instrument-27 (SpI-27). A secondary aim was to psychometrically evaluate this instrument in a sample of individuals with chronic illness (n=249). Methods: A two-phase design was adopted. Phase one consisted of the development of the SpI-27 based on item generation from a concept analysis, a literature review, and an instrument appraisal. The second phase established the psychometric properties of the instrument and included: a qualitative descriptive design to establish content validity; a pilot study to evaluate the mode of administration; and a descriptive correlational design to assess the instrument’s reliability and validity. Data were analysed using SPSS (Version 18). Results: Results of exploratory factor analysis concluded a final five-factor solution with 27 items. These five factors were labelled: Connectedness with Others, Self-Transcendence, Self-Cognisance, Conservationism, and Connectedness with a Higher Power. Cronbach’s alpha coefficients ranged from 0.823 to 0.911 for the five factors, and 0.904 for the overall scale, indicating high internal consistency. Paired-sample t-tests, intra-class correlations, and weighted kappa values supported the temporal stability of the instrument over 2 weeks. A significant positive correlation was found between the SpI-27 and the Spirituality Index of Well-Being, providing evidence for convergent validity. Conclusion: This research addresses a call for a theoretically-grounded instrument to measure spirituality.

Global and local perceptual style, field-independence, and central coherence: an attempt at concept validation

Historically, the concepts of field-independence, closure flexibility, and weak central coherence have been used to denote a locally, rather globally, dominated perceptual style. To date, there has been little attempt to clarify the relationship between these constructs, or to examine the convergent validity of the various tasks purported to measure them. To address this, we administered 14 tasks that have been used to study visual perceptual styles to a group of 90 neuro-typical adults. The data were subjected to exploratory factor analysis. We found evidence for the existence of a narrowly defined weak central coherence (field-independence) factor that received loadings from only a few of the tasks used to operationalise this concept. This factor can most aptly be described as representing the ability to dis-embed a simple stimulus from a more complex array. The results suggest that future studies of perceptual styles should include tasks whose theoretical validity is empirically verified, as such validity cannot be established merely on the basis of a priori task analysis. Moreover, the use of multiple indices is required to capture the latent dimensions of perceptual styles reliably.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.