Funding special education provision by means of discriminant function analysis

This thesis is concerned with the development of a funding mechanism, the Student Resource Index, which has been designed to resolve a number of difficulties which emerged following the introduction of integration or inclusion as an alternative means of providing educational support to students with disabilities in the Australian State of Victoria. Prior to 1984, the year in which the major integration or inclusion initiatives were introduced, the great majority of students with disabilities were educated in segregated special schools, however, by 1992 the integration initiatives had been successful in including within regular classes approximately half of the students in receipt of additional educational assistance on the basis of disability. The success of the integration program brought with it a number of administrative and financial problems which were the subject of three government enquiries. Central to these difficulties was the development of a dual system of special education provision. On one hand, additional resources were provided for the students attending segregated special schools by means of weighted student ratios, with one teacher being provided for each six students attending a special school. On the other hand, the requirements of individual students integrated into regular schools were assessed by school-based committees on the basis of their perceived extra educational needs. The major criticism of this dual system of special education funding was that it created inequities in the distribution of resources both between the systems and also within the systems. For example, three students with equivalent needs, one of whom attended a special school and two of whom attended different regular schools could each be funded at substantially differing levels. The solution to these inequities of funding was seen to be in the development of a needs based funding device which encompassed all students in receipt of additional disability related educational support. The Student Resource Index developed in this thesis is a set of behavioural descriptors designed to assess degree of additional educational need across a number of disability domains. These domains include hearing, vision, communication, health, co-ordination (manual and mobility), intellectual capacity and behaviour. The completed Student Resource Index provides a profile of the students’ needs across all of these domains and as such addresses the multiple nature of many disabling conditions. The Student Resource Index was validated in terms of its capacity to predict the ‘known’ membership or the type of special school which some 1200 students in the sample currently attended. The decision to use the existing special school populations as the criterion against which the Student Resource Index was validated was based on the premise that the differing resource levels of these schools had been historically determined by expert opinion, industrial negotiation and reference to other special education systems as the most reliable estimate of the enrolled students’ needs. When discriminant function analysis was applied to some 178 students attending one school for students with mild intellectual disability and one facility for students with moderate to severe intellectual disability the Student Resource Index was successful in predicting the student's known school in 92 percent of cases. An analysis of those students (8 percent) which the Student Resource Index had failed to predict their known school enrolment revealed that 13 students had, for a variety of reasons, been inappropriately placed in these settings. When these students were removed from the sample the predictive accuracy of the Student Resource Index was raised to 96 percent of the sample. By comparison the domains of the Vineland Adaptive Behaviour Scale accurately predicted known enrolments of 76 percent of the sample. By way of replication discriminant function analysis was then applied to the Student Resource Index profiles of 518 students attending Day Special Schools (Mild Intellectual Disability) and 287 students attending Special Developmental Schools (Moderate to Severe Intellectual Disability). In this case, the Student Resource Index profiles were successful in predicting the known enrolments of 85 percent of students. When a third group was added, 147 students attending Day Special Schools for students with physical disabilities, the Student Resource Index predicted known enrolments in 80 percent of cases. The addition of a fourth group of 116 students attending Day Special Schools (Hearing Impaired) to the discriminant analysis led to a small reduction in predictive accuracy from 80 percent to 78 percent of the sample. A final analysis which included students attending a School for the Deaf-Blind, a Hospital School and a Social and Behavioural Unit was successful in predicting known enrolments in 71 percent of the 1114 students in the sample. For reasons which are expanded upon within the thesis it was concluded that the Student Resource Index when used in conjunction with discriminant function analysis was capable of isolating four distinct groups on the basis of their additional educational needs. If the historically determined and varied funding levels provided to these groups, inherent in the cash equivalent of the staffing ratios of Day Special Schools (Mild Intellectual Disability), Special Development Schools (Moderate to Severe Intellectual Disability), Day Special Schools (Physical Disability) and Day Special Schools (Hearing Impairment) are accepted as reasonable reflections of these students’ needs these funding levels can be translated into funding bands. These funding bands can then be applied to students in segregated or inclusive placements. The thesis demonstrates that a new applicant for funding can be introduced into the existing data base and by the use of discriminant function analysis be allocated to one of the four groups. The analysis is in effect saying that this new student’s profile of educational needs has more in common with Group A than with the members of Groups B, C, or D. The student would then be funded at Group A level. It is immaterial from a funding point of view whether the student decides to attend a segregated or inclusive setting. The thesis then examines the impact of the introduction of Student Resource Index based funding upon the current funding of the special schools in one of the major metropolitan regions. Overall, such an initiative would lead to a reduction of 1.54 percent of the total funding accruing to the region’s special schools.

Assessing the legitimacy of humanitarian intervention : purpose, authority and means

This study looked at military deployments that seek to promote human rights, including operations in Somalia, Rwanda and Kosovo. While a legitimate humanitarian purpose and international authority for these missions can be demonstrated, finding the appropriate means of action - or how to best conduct the operation - remains very difficult, ensuring similar future missions will remain controversial.

On migrative means and copulas

In this short work we extend the results of J.Fodor and I.J. Rudas [6] characterizing migrative triangular norms, to quasi-arithmetic means. We use idempotisation construction to obtain quasi-arithmetic means migrative with respect to fixed parameter a. We also obtain the necessary and sufficient condition for a migrative triangular norm to be a copula.

Some results on Lipschitz quasi-arithmetic means

We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k.

Assessing sustainability : a technical fix or a means of social learning?

The contextual nature of sustainability makes it extremely difficult to measure. Across the world each region has a specific environment and history that has shaped values and perceptions of the local community. In response, a wide range of tools has been developed that employ differing techniques to measure sustainability. These have a range of applications from global to site-specific scales. However, it is yet to be resolved whether assessments made using these tools reflect a technical focus with no close links to the knowledge and perceptions of stakeholders, community and management decisions, or whether the assessments reflect the knowledge and perceptions of local stakeholders and the community. In the southwest region of Victoria, Australia, a sustainability index called AIRS (An Index of Regional Sustainability) has recently been developed. This tool is based on indicators selected by stakeholders and considers relationships between the indicators. The aim of this paper is to report an ex-post evaluation of the AIRS sustainability assessment conducted at a subcatchment scale. The evaluation assesses AIRS's ability to assess regional sustainability and compares and contrasts the subcatchment assessments with the knowledge and perceptions of stakeholders and the community. A participatory approach that acknowledges key stakeholders was used for the evaluation process. Representatives from four stakeholder groups were interviewed to elicit their views of the AIRS assessment, its relevance, quality, applicability and priorities for future development. Strengths and weaknesses of AIRS are revealed and its contribution to social learning is highlighted.

On generalized bonferroni means

In this paper we investigate modeling capabilities of Bonferroni means and their generalizations. We will show that weighted Bonferroni means can model the concepts of hard and soft partial conjunction, and lead to several interesting special cases, with quite an intuitive interpretation.

Beyond Simon’s means-ends analysis : natural creativity and the unanswered ‘why’ in the design of intelligent systems for problem-solving

Goal-directed problem solving as originally advocated by Herbert Simon’s means-ends analysis model has primarily shaped the course of design research on artificially intelligent systems for problem-solving. We contend that there is a definite disregard of a key phase within the overall design process that in fact logically precedes the actual problem solving phase. While systems designers have traditionally been obsessed with goal-directed problem solving, the basic determinants of the ultimate desired goal state still remain to be fully understood or categorically defined. We propose a rational framework built on a set of logically interconnected conjectures to specifically recognize this neglected phase in the overall design process of intelligent systems for practical problem-solving applications.

Means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties. We also discuss which of them coincide with the Cartesian product of the standard mean and median.

Image reduction using means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

Fast computation of trimmed means

We present two methods of calculating trimmed means without sorting the data in O(n) time. The existing method implemented in major statistical packages relies on sorting, which takes O(n log n) time. The proposed algorithm is based on the quickselect algorithm for calculating order statistics with O(n) expected running time. It is an order of magnitude faster than the existing method for large data sets.